Disclaimer: I've only finished Blue Lions and currently playing again as Black Eagles. My difficulty complaints are just that, complaints. I loved the game all the way through and I think it is one of the best FE games ever made, and one that brings much needed changes to the entire sRPG genre.
Replaying the school session confirms a suspicion I had while playing BL the first time; The main chapters before the time skip are not difficult even on hard. They can certainly be challenging as the game starts throwing monsters and promoted units at you at the same time but it rarely changes how you play.
Post time skip the difficulty seemingly increases, with more enemies, more monsters, and enemies using gambits more frequently, but your units are so strong (especially Dimitri in BL) that it kind of doesn't matter. As the main chapters progress, the game does get a bit harder when maps have fast enemy units with ridiculous AS that double everyone except your fastest unit. However, you have so many tools available to deal with these threats that they are always easily manageable. Moreover, monsters become non-threatening after a certain point, even though the game tries hard to spam you with them, as half of your units can solo them (squishy units are obviously still vulnerable). Some of the paralogues are actually more difficult than the majority of main story chapters. They also have more varied and interesting objectives.
I believe the reason it feels easy even on hard comes down to a few things ( in no particular order ) :
i) You get too many levels by just going through the motions. If you just follow the way the game suggests for you to play, your units end up over leveled. Honestly, you just get way too much exp. The saint statues make this even worse.
ii) Paralogue rewards are broken.
iii) Some of the units you get are busted (e.g. Petra/Felix/Sylvain) and since you have them from the very start, you can train them to be incredibly strong. For this reason, I expect GD to be the hardest route if you just stick to the GD students. Also, Catherine and Shamir are too powerful for how easy it is to recruit them.
iv) The game is obviously not balanced around micromanaging the students at the school phase. You can get really high weapon ranks quite early for little effort and no combat.
v) All main story maps are rout/defeat commander. This makes the majority of chapters amenable to rushing by using warp and/or stride.
vi) You have way too many charges of Divine Pulse, even without the saint statues. You can be super reckless and the game does not adequately punish you for it. This is similar to a problem Echoes had with the turnwheel.
vii) As always, high movement trivializes certain aspects of the game. The movement gambits are too strong (it should have been +2 move or something).
viii) Fliers are too strong, as always. Several chapters that have impassable terrain would be significantly harder if fliers weren't able to cross the map with ease.
ix) The online features break the gameplay loop imo. You get so much exp for standing in the yellow tiles and there are always a few per map (which is about ~1 level).