You're talking about the intellectual content of the book. I'm with you.
And I'm not arguing, I'm just trying to make sure we're talking about the same things before we embark on our next great debate.
Then we need to circle back, because I'm not sure what you're saying. Your talking about how Player's Handbooks are shelved in some nominal library and using that to saying something about its genre. I'm not following, this seems a very strange line of argument to me.
We've moved on from that discussion. We're talking about tropes now.
Lawful good paladin is the trope, not paladin. The rules for personality and background show you how to play up tropes and be rewarded for doing so.
There's a lot of nestled assumptions here.
1) BIFTs are rewarded
2) If you are playing a lawful good paladin, Chapter 4 shows you how to do this.
3) Paladins are lawful good.
Starting from the bottom, 3) isn't true anymore. There are no requirements that paladins be lawful or good.
2) There are no backgrounds or BIFTs that are tagged "for paladins." In fact, if I follow one of the options, I can roll for BIFTs and end up with chaotic and evil tagged BIFTs for my paladin. This is playing by the rules, so Chapter 4 can't be said to actually show you how to play a lawful good paladin (again, note the assumption with 3)). I can have a criminal background Paladin with evil tagged ideals. Sounds like some fun!
Instead, 2) relies on the assumption that a paladin is 3) lawful good and that the player already knows what this means and so can make selections based on this. However, as noted with 3), there's no guidance for the paladin class that it be good or lawful, so a new player, not familiar with this trope, will not find any help in Chapter 4 to align to this trope because Chapter 4 doesn't say anything at all about paladins being lawful good or how you would do that.
Finally, your 1) is still not correct. I just pointed out how Inspiration is entirely up to the GM by the rules, and runs the gamut from never being awarded to being awarded for leveling to being awarded for completing a quest or adventure to being awarded at the beginning of the session to being awarded when the GM thinks you've done a BIFT well enough. All of this is within the rules and guidance for Inspiration -- all of it. Chapter 4 tells a player they
may be rewarded for a BIFT, but to ask the GM to find out how they're doing it. This isn't the virtuous cycle you're assuming, and, quite often, it's not done this way at all with a large chunk of the community ignoring BIFTs and Inspiration altogether -- and doing so according to the rules of the game.
Finally, Paladins being lawful good isn't a defining trope for the D&D genre. (If anything, Lawful Stupid Paladins are more identifiable as D&D, but I'd not put it there.) You can remove Paladins from the game entirely and not touch the defining tropes of D&D. Absence of the Paladin doesn't suddenly make D&D not D&D. Your earlier statement about alignment is much more on target, but not things like lawful good paladins but rather the alignment structure itself. Again, however, 4th and 5th have worked hard to neuter this, and I'm not sure it's actually done the D&D genre much harm. It's certainly reduced the impact of the memes based on alignment for the newer generations of players.
I think that Van Richten's Guide to Ravenloft and Rising From the Last War were both great campaign sourcebooks. How did they fail to deliver on theme?