Figuring out the demographics of medieval armies, especially urban militia deployments is notoriously tricky, it's something I've looked into for a long time and I can offer some observations and a few data points, though I don't think we know enough to say anything definitively. I also think you have to be cautious comparing across regions and estates, in particular comparing England to the continent or urban to rural. There are big differences there.
That said, I do not think 2,000 crossbowmen is an unheard of number. It's large, but not beyond the pale. I believe you will find that many crossbowmen of some type in armies of the 15th century, including Bohemian, Flemish, Swiss, Burgundian, Hungarian, German and probably Italian armies. The best places to look for records for this sort of thing would probably be the Swiss chronicles, the letters of Matthias Corvinus vis a vis the
Fekete Sereg or Black Army of Hungary, which had a large proportion of shooters, in the annales of Jan Dlugosz as he often talks numbers and knew military matters, and from the records of the Teutonic Order.
The best later 15th Century Italian source I can think of would be
Piccolomini, who traveled around quite a bit as a spy and diplomat prior to becoming Pope, was an extremely prolific writer and understood military matters.
There are a couple of specific issues to break down here, as several are kind of tangled together, so I'll take a stab at unraveling one or two of them.
Urban Militia Demographics
This is tricky to unravel. You'll read in the urban chronicles of the larger towns over and over, that they deploy 3,000 men or 5,000 men for this or that, and they might distinguish horsemen from footmen, but it's fairly rare to get details on the composition. But you can find some examples. The conundrum for the cities is that if they deploy more troops, they get a better and more loyal army, but conversely, the army itself will be harder to control and will make more political demands if they win. The classic example of this is in Flanders after Golden Spurs, the guild militias forced their way into the town councils of Bruges, Ypres and Ghent. The other problem with guild militia is that they had a lot of political power even in the field, so they would routinely refuse to go beyond a certain distance from the city walls, to stay out overnight, or especially and in general, to go on offensive expeditions unless they saw a direct benefit. This was a major problem especially when town militia were fighting for a prince.
The second problem was the one you were alluding to for Florence, if they took heavy losses in their highly skilled artisans and merchants, it could send the town into an economic death-spiral. This almost happened to Ghent after a couple of their big defeats in the 14th and 15th Centuries, and in many other places. For example in the chronicle of Bremen it mentions that after a major defeat (during which an army of 2,000 men were wiped out in the Dithmarschen region of Frisia), grass was growing in the street for years before enough of a new generation came of age and enough immigrants came in to town to replace the losses. And that was a small army that was killed off.
So the solution or compromise for the towns was to mobilize a small force as the hard core of a larger army, and the army itself was mostly made up of mercenaries. A classic example that is often repeated comes from some records from Regensberg in the 1420's, as part of the general deployment against the Hussites of Bohemia. This excerpt was translated by Hans Delbrück and has subsequently been repeated by many others, often without attribution. The Regensburghers, who were probably not overly enthusiastic about the overall mission, provided a very well equipped and supplied force of 248 men. Of that number roughly two thirds (160 men) were fighters, and the others were skilled specialists of the type very helpful to military efforts like smiths, leatherworkers, cooks, butchers, pike-makers etc. The fighters consisted of 73 "constaffler" horsemen, mostly lancers but including about 20 mounted crossbowmen; 71 infantry crossbowmen;, and 16 hand-gunners. All of the fighting men were very well armored and kitted out. They came with 41 wagons of supplies which included 6,000 crossbow bolts, 300 fire-bolts, 19 extra handguns, 6 cannon, 300 lbs of cannonballs and 200 lbs of lead shot, along with tents and field fortification gear, and enough food and horse-fodder for six weeks.
This force of 248 men marched toward Bohemia and met up with a larger army of 1,500 Bavarians, of whom 500 were cavalry (likely Bavarian gentry) and 1000 were infantry, probably peasants. Then the whole force continued into Bohemia to their likely doom.
Sometimes these small, hard core urban militia units would combine with feudal armies as in the above case, but more often they would be combined with mercenaries, which further complicates matters.
Who were the mercenaries?
Medieval warfare was dominated by mercenaries. This was the role the Genoese militia was playing in France not just in
Crecy but in several battles. Sometimes that was how it went - mercenaries would be contracted from a condottiere, or hired in one big group from one place, like one of the Swiss, Italian, or Bohemian towns. But more often the makeup of mercenary armies was something of a mystery, and many of them seemed to be hired directly by town authorietes for a specific campaign.
There have been some attempts to analyze and track down the names of some of these people, and in a couple of cases it turns out that as many as 25% may come from the town doing the hiring, and people who may be in the militia, but they would sign up as mercenaries instead. Others came from the local area, smaller towns and villages which may still have citizenship or 'paleburgher' status with the larger town organizing the expedition, and others come from more distant towns and regions.
Certain areas like the Swiss city-states actively cultivated their hinterland as pools for this kind of manpower and most towns, though especially the Swiss, conducted frequent enough expeditions and military raids etc. that they were used to fighting together. With medieval armies, especially those with disparate estates and factions, the number of times they fought together was one of the key determinants of success. This is the key difference between the success of the highly international Fekete Sereg in fighting the Turks, compared to the hastily thrown together Feudal armies such as were annihilated at Nikopolis etc.
These units were still routinely led by town political figures, bürgermeisters and members of the town council, who had to carefully balance the makeup of their forces, so that they had some degree of predictable loyalty as well as enough highly skilled fighters, while not putting too many of their guys at risk. The risks for the leadership themselves seemed to be quite high. For example, when they sent a small, hard core unit to storm a castle occupied by French Armagnac mercenaries in Alsace in 1444, the forces of Strasbourg lost two burgomeisters, one of whom was shot and another thrown off a ladder, in the otherwise successful action. I got into the details of that war
here in an old essay on HROARR.
Crossbowmen vs. crossbowmen
Another conundrum for modern researchers and historians when looking at specific troop types like "crossbowmen", is that there was a lot of variety in terms of the demographics, training, and kit which made a big difference in what the term actually meant. Just as we know very well that a 'horseman' can be anything from a heavily armed knight or constaffler, to a demi-lancer, mounted archer, or light cavalry like a Hungarian hussar or Uhlan, 'crossbowmen' could also mean a variety of troop types.
By the late medieval period, as helpfully delinieted by Teutonic Knights expert Sven Ekhdal
in his oft-linked 1998 essay, a marksman or crossbowman could mean several different things representing different estates or demographics, and far different capabilities. It could mean barely trained peasant levies using solid wood prod crossbows spanned by hand (and considered suitable only for static defense of fortifications), to more trained militia armed with steel or composite prod crossbows of medium power, to skilled experts, men who had won wreaths in the
schützenfest, armed with deadly 'half ton' or 'stinger' arbalests of 1,000 lb draw or more, and accompanied by a paviseman and maybe a spare crossbow. The latter guys were being paid as much as 11 gulden per month by Mathias Corvinus. Or they could be mounted crossbowman of the equivalent rank as a lancer, or specialists with giant wall crossbows meant originally for sieges, but brought out into the field by the Bohemians and others on their war wagons, along with the hand-büschen, the arquebus and the field gun.
So the devil is definitely in the details, both in terms of demographics and the type of troops. Always interesting to discuss these things but we must be cautious of hastily drawing conclusions. There is a great deal more research to do.