10th-11th century would mean even less horse armors. Less archers too so less need for those armors, at least in West.
And of course 10th-11th century they didn't use pikes or glaives etc. Lances wouldn't be couched lances of later time. Instead they would be held with a one-handed over-the-head grip. Longbow as weapon of war was late 12th century thing too.
So if Bannerlord is about 10th-11th century, there is lot of things that go wrong. So based on that I would think that it is about later times. Man from 13th century could use arms and armors from 11th century, but for a man from 11th century it would be lot harder to find equipment from 13th century.
In this game horses are tanks. They are WAY harder to kill than they would be realistically. Horses can't take 2 handed axe hits to heads any more than humans and it wouldn't take many longbow arrows to kill a horse. People hunt elks today with bows and they don't do it by shooting it with dozen arrows.
And yeah losing horse in wrong spot can be dangerous. But realistically it would be way more dangerous. Every year ~100 people die in riding accidents and even if you wouldn't die it would be easy to have leg pinned under that horse when it falls. Would be certain death if it would happen in middle of a battle. And of course horses are not machines and doesn't like to get wounded. Most likely horse will do something when it is wounded so I think that that riding/vigor/control check should be needed every time horse is wounded.
It is balance problem if cavalry have all advantages horse can give but no weaknesses. Some knight fought on foot and they had good reason for that. Horses are not tanks and it was very dangerous for knight when his horse was wounded and of course it is not easy to control horse when your both hands are occupied with weapons. Controlling a horse with a glaive, for example, is far too easy.
Uh...I hate to say it but I think you're perhaps suffering from excluding everywhere else but Britain, maybe? Longbows have been around well before the medieval period. Earliest instance I know goes back several thousand years prior to that, in fact. The famous ice-borne mummy, The Ice Man or "Otzi," was found with his yew longbow. It was six feet long. Further there's evidence in Scandinavia of longbows being used basically for the entire historic record we have for those cultures.
As to horse armours, I don't think we have anything too out of the ordinary here. Notably the Byzantines the Imperials are partly patterned after outfitted their Cataphracts the game's Cataphracts are definitely patterned after with armour. I admit I'm dubious of a couple pieces in the game, but all in all it's not too egregious. I'm thinking especially of the Mail and Plate barding, I think it's called.
Couched lances were an initial controversy in this game for the lack. I have to admit, I find the introduction of couching somewhat questionable, but then it comes down to whether the advanced equipment later knights had to aid in this was actually necessary, or whether some rudimentary form of couching might have existed without it -- really, it's a simple technique where you brace the polearm to the horse in much the way one would to the ground, so it's plausible even if in my opinion unlikely. For my part, I find this tolerable because couched lances are much harder to hit with in Bannerlord than in Warband.
Finally, as to the ability for horses to tank. They are quite a bit tougher than humans, trust me. That said you are right about the arrows they can take as well as two-handed weapons. Both need to hit properly, though. Arrows in the right place will take down a horse, but I think most bow-hunters will attest to how difficult it is to take an animal down by arrow, and how much placement matters. To the two-handed weapon in the head, that's an act of timing and precision when targeting an animal that is moving its head while propelling its body at high speed past you -- not impossible, but also quite the hit to rally off while you're standing basically in the path of this charging animal -- but I digress. With perks, you absolutely can one-hit a horse with two-handed weapons, two hits at most. There are perks to quite dramatically increase the damage done to mounts with two-handed weapons, so this reflects the level of skill to take down a massive animal so quickly. I think I'm okay with that, though I'd be interested in what balanced solutions that take those perks into account there might be.
Cavalry does not have all the advantages. I don't honestly know how that can be argued unless other playthroughs haven't been attempted. I actually find far more advantage with an all-archer party. That's my current playthrough, and me and my Fians are absolutely brutal. I have never ended battles as fast with cavalry. Another playthrough I have that absolutely leaves my cavalry playthroughs in the dust is a character whose party is primarily made up of Battanian Skirmishers. They take longer to get across the field, but this swarm decimates that field. The biggest disadvantage I see in cavalry is their post-charge run out, as well as when they get stopped -- they have no support when this happens, and simply get swarmed and taken out. Cavalry takes a lot longer once the fighting starts to end that fight. My archers end it before the opponent can even reach them to do damage usually, and my skirmishers are too good at supporting one another in battle for the enemy to get the upper-hand, and their javelins mean they're able to engage constantly, as long as I don't let them fire them all off in the opening. I really don't think it's as poorly balanced as some are saying, or else my cavalry games should be the ones dominating. Even when I've played horse-archers, they're so painfully slow at taking out the enemy. That's a big disadvantage when taking out the enemy is the objective.
