The Pike and shot period often tends to b described as a case of rock-paper-scissors where horse beats shot beats pike beats horse. However the importance of pikemen still seems to be emphasized quite a bit for supposedly having a primarily defensive role, and the maurician-inspired pike and shot formations of the 17th century definitely seem to be optomized more for fighting infantry than for defending against cavalry.

I wonder if perhaps a better way to describe the relationship between pike and shot is that in skirmishes between small numbers of infantry on each side, a force with firearms only is much more useful. However in a battle involving very large numbers on each side an infantry force with shot only is generally at a disadvantage against a force with a large proportion of pikes or only pikes, even discounting any cavalry. This perhaps finally changed when faster-firing flintlocks and bayonets come about.

La Noue, who blamed French Huguenot defeats on the lack of armored pikemen uses this example to explain why a one on one duel doesn't determine the outcome of pitched battles:

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It is as if a man should say, that because in the field one harquebuzier may kill a pike man armed with his corcelet, it followeth that in pitcht fieldes the harquebuziers should ouerthrow the battailes of pikes: which neuerthelesse falleth out cōtrarie, for it is certaine that for the most part those battailes do giue the victorie.

Matthew Sutcliffe, though more an academic than a soldier, similarly concluded from studying recent battles that shot was more useful in a skirmish than in a large battle.

Robert Barret, in his 1598 "Theorike and Practike" seems to offer a dissenting opinion, instead again citing cavalry as the main reason shot must be supported by cavalry:

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As the armed pike is the strēgth of the battell, so without question, is the shot the furie of the field: but the one without the other is weakened the better halfe of their strength. Therefore of necessitie (according to the course of warres in these dayes) the one is to be coupled & matched with the other, in such conue∣nient proportion, that the aduantage of the one may helpe the disauantage of the other. For a stand of pikes, though neuer so well armed, being charged & assailed with the like, or a lesse number of shot, by euery mans iudgement would haue the worse, & not able to abide the field, vnlesse they had shot, to answer their enemies shot. In like sort, any troupe of shot, though neuer so braue & expert, being in o∣pen field, hauing no stand of pikes, or such other weapō, nor hedge, ditch, trench, or rampier, to relieue and succour them, could not long endure the force of horse, especially Launciers.

However, it might be that he's talking in general about a smaller stand of pikes than La Noue is talking about. Elsewhere he does often talk about fighting pikes with pikes and he repeatedly emphasizes again that pikes are still the "strength of the battle" and that victory is achieved by defeating the enemy's pikemen, not his musketeers:

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. . . for hee is but a foolish shot, that shooteth at, or among light skirmishers, where he may discharge vpon the body of his enemies battell, which standes thick together, and is a fayre marke to shoot at; for the armed pikes once ouerthrowen, which is the strength of the field, the victorie by all likelyhood is like to ensue.

On the subject of battles often being decided before the infantry comes into contact, he again interjects the importance of a strong backing of pikes:

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And againe it is rarely seene in our dayes, that men come often to hand-blowes, as in old time they did: For now in this age, the shot so employeth and busieth the field (being well backed with a resolute stand of pikes) that the most valiantest and skilfullest therein do commonly import the victorie, or the best, at the least wise, before men come to many hand-blowes.

Perhaps the fact that engagements were more often decided before contact has more to do with the fact that a charging block of pikemen disordered by gunfire were less willing to charge home into a well-ordered pike square of the enemy's than they would be against a force of unsupported arquebusiers.

Robert III de La Marck (Florange) recounted how 400 Swiss halberdiers routed 800 arquebusiers at Novara 1513. Of course, those arquebusiers had already been shooting before this, so their pieces probably weren't in prime condition when the halberdiers attacked.

I was never a specialist in the 16th century, but you might want to look at how these debates continued into the 17th and 18th century.

If you have an academic library near you, there is an English-language book which looks at French infantry theory from the late 17th century to the days before the French revolution. I read it 10 years ago in Canada, and I don't have any idea how to find it in the new country though :( But it gives an English-language summary of how people proposed to deal with the basic problem that shot could kill many soldiers but rarely sent whole armies running like a charge with swords, pikes, or bayonets could (while just sending men on foot with sharp pointy things into a hail of bullets did not work either).

Lots of early pikemen where partaly shot resistet, so armour was useful aginst long range fire.
And givee the short effective ranges of most guns, one could often find your enermy to be all most out of shot or panicked when the pike entered the battle.

In close terrain muskets areforced to hold there fire and only start fireing at short ranges, contering both armour and the poor training of most musketeers.