For the first point, there's the Byzantine army of the 11th century in which according to the Taktika and Praecepta militaria the standard "hoplites" were supposed to be armed with shields almost 5 feet tall and long spears between 19-23 feet long. https://www.reddit.com/r/AskHistorians/comments/6h7rtv/in_many_medieval_strategy_games_the_army_is/diwgg4e/
As for the second point, here are some thoughts in no particular order
-We might be overestimating how much equipment is too encumbering based on the soldier's percieved role. The byzantine example in particular seems to represent a peak "heavy infantry as the defensive arm" mindset, with the spearmen serving as primarily pretty much a mobile wall or fortress while the actual attacking is done by either cavalry or light skirmishers, who would then retreat back behind the heavy infantry for protection. This is how the writings of vegetius mostly view heavy infantry and also seems to bear a lot of similarities to how pikemen and dedicated heavy infantry tended to be used by various nations aside from the Swiss. The aggressive swiss pike columns were not the norm. And if a foot soldier is expecting to spend most of the battle just standing in one place, then he can spend much of that time with his long pike or large shield resting on the ground. with a two-handed weapon he probably wouldn't have his shield strapped to his arm at all and instead possibly proped up on the ground, or else slung from the neck and shoulder like the macedonians supposedly did. "and with a slight wrying of the body, and lifting up the right shoulder, whirled their target, hanging at their back, upon the left shoulder, that stood next the enemy in the charge."
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-As a caveat, while you can sometimes find sources that make a clear distinction, i tend to be skeptical about terminology remaining 100% consistant between different authors, regions and periods. So it might be that we're seeing is a transition between an era where to protect a pike formation against arrows you could create shields which were large, but still fairly lightweight and maniable, and an era in the 15th century where the increasing power of crossbows and firearms created a need to more often use to much thicker, heavier shields which had to be propped up on the ground as a stationary mantlet, or else carried by dedicated shield troops stationed in front to provide cover for those armed with crossbows or two-handed weapons. In the Heavy Arbalest thread a while back Jean posted this video which gives an example of just how elaborate the construction of some late medieval pavises could get: https://www.youtube.com/watch?v=G2Rl9DLUfao
however while the idea of trying to protect soldiers from missiles with shields was eventually largely abandoned in the face of heavy gunpowder artillery, there are examples where it seems to have continued to be a recommended tactic at times against large numbers of archers in particular. From the English translation of Jacapo di Porcia's late15th century Preceptes of Warre:
| Quote: |
| What is to be done when thyne enemyes be moost parte archers.
When our enemyes be for the mooste part archers, then set aganyst them, men fenced with tergates, whych sort of soul∣dyours be sometyme in the hostes of the East partie. And by this pollicie thyne army shalbe out of theyr daunger. |
There's also the case of late 16th century ireland. Where, as the english longbow was increasingly being seen as obsolete on the continent, there started to be a pattern of english archers being redeployed to the wars in ireland with the idea being that they should still be able to do good work against the very poorly equipped irish rebels. However, according to Barnabe Rich, the irish were still able respond by creating large wicker shields to protect themselves:
| Quote: |
| . . . [the irish] invented targets made of small wickers, like basket liddes, which weighing not above two pownd weight, would cover them from the toppe to the toe, and sometimes with their mantles hanging loose about their armes, which was the cause that our captains of that countrey, long sithence have converted all their bows to calivers, and from that time have so continued. |
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-Lastly, it's probably worth keeping in mind that in the late middle ages, for all but the poorest light infantry you would probably rarely expect to see a "marius's mules" situation where each soldier would actually be expected carry all his own arms and supplies while on campaign. Instead, even many of the infantry would likely had to have at least one servant, a draft animal, or at least shared a cart on which they toss most of their weapons and armor while on a long march. So in cases where soldiers were supposed to have more weapons than one could reasonably be expected to fight with at the same time it might be that it's purpose was just to help ensure that the army had a sufficient quantity of each one, and then before a given engagement the soldier would get to pick and choose whether he wanted to fight with his two-handed polearm, his pavise, or something else and then leave the rest behind with the baggage depending on whether it was a skirmish, a siege, or an open field battle.