Other adventurers, no? In the history of the game world, other adventurers have fought these things, survived, and made sure the knowledge gets passed down to the next generation for further use. Unless you are running a campaign where the PCs are the only adventurers who have ever been, I'm not sure why this is so weird.
No, but I can't see why this knowledge wouldn't get passed around the way any other knowledge gets passed around. They may not be dubbed "Adventurer's Colleges" per se, but you can bet that any university in, say, Geoff or Sterich in the Greyhawk world has pretty comprehensive knowledge of giants, given their history. Attending the university of magical arts in Greyhawk proper certainly gives the opportunity to make knowledge checks about a whole range of magical creatures, etc.
I do not necessarily disagree with you.
But in today's real world, information is shared very quickly on the Internet (and even on TV). Even before the Internet, there were books for over 500 years. Before that, the vast majority of information is even today lost in antiquity. And even what we have today and take for granted as being correct and accurate is probably not so. People then are the same as people now. Scholars today sometimes cheat or take shortcuts or enhance their own reputation by outright lying. How much more do you think that happen 500 to 4000 years ago in the real world when the ability to verify the information being written down was limited?
In a (presumably) medieval world of magic, accurate monster information would be shared and preserved mostly by scholars, scribes, archivists, and clergy. Much of it, just like in the real world, would be protected and guarded, and not necessarily easily accessible by PCs. In the Forgotten Realms, Candlekeep is that world's equivalent of the Library of Alexandria.
So one issue that I have with knowledge checks is that at many or even most tables, they tend to be 100% accurate. There is no chance of a fumble or failure. No misinformation (and players roll at many tables, so they know whether they rolled low or high). Just like with climbing, there should be a penalty (i.e. false information) for a low roll. Most known semi-accurate information on monsters should be acquired via sages, not necessarily in the heads of PCs. PCs should have some information on some monsters, but some significant percentage of it should just plain be false info.
I don't have a problem with a knowledge check per se (I do think that the 4E monster knowledge check rules were too liberal). I just think that the rules for it should be something like:
1) DM rolls in secret.
2) If an extremely low roll is made, false information is supplied.
3) A roll is not made for every PC (for simplicity). Maybe a +1 is added for each PC beyond the first to a max of +5 (i.e. the equivalent of advantage).
3a) If a roll is desired for each PC, then of course, the odds of rolling low will increase the chance of fake information. In that case, the DM might not need to roll, the players can roll. In that case, the DM does not tell individual players what their PC knows, he just tells the group what the group knows, both false and true information.
4) The DC is based on monster level (i.e. higher level monsters tend to outright kill anyone and hence by default, prevent detailed info from getting out) and monster rarity (more info should be known about common monsters than rare monsters).
5) Based on how high above the DC the roll is made, multiple pieces of information and more accurate information is supplied. Based on how low below the DC the roll is missed, less accurate information is supplied (and possibly multiple less accurate pieces of info for a really low roll). A mid-range roll might supply both accurate and inaccurate information.
I didn't see this post at first, but there is in fact a logical answer for 5e:
Volo's guides.
FR literally had (has?) a publication that went around to catalog and describe all the weirdo monsters and stuff in the Realms for adventurers.
Heck, there are even the Van Richten's Guides for Ravenloft, of all places!
Which Volo guides went into detail on monsters? Magic items and spells, sure. Locals, sure. Monsters? There might be a mention here and there, but hardly detailed info on monsters unless I missed a book.
Many of his guides were about rating how good taverns were, info on towns, etc. It was DM location detail info.
Volo's Guides are for the DM, not for PC in game knowledge per se. They are the result of a real world gaming company selling content.