I thought that fire emblem was all about LTC, not infinite exp abusing.
This game even has the turn it took you to clear a chapter.
Mostly correct. It's about efficient play. Grinding to max level on the first map isn't skillful and will give you a massive turn count, which this game does penalize you for by giving you less gold as a clear bonus. Ranked runs generally rank you not just on turn count, but on exp and gold earned too. Doing something like that would also ruin your combat rank in FE games that have it, as you get a worse combat rank for every battle you participate in that doesn't result in a "win" (killing the enemy.)
That said, I have nothing against the excelblem style of play, it just seems really strange to do it in a super easy adult game and not in a hardcore challenge run where you need to do exploits like that in order to have a chance. If you want to get infinite exp in this game, just click the give up button and you'll restart the map with all your exp retained (though the game does keep track of how many times you do this too.) Like sure, I've babied Ilyana in Radiant Dawn with Blossom to 20/20/20 before but there's a difference between going out of your way to make a normally bad character good at the cost of efficiency because you like them and grinding Gordin to level 20 on the first boss that has no ranged attacks because you want to clear every map after that effortlessly. Just play on easy mode if you just want to steamroll the game from the start. Or use Chrobin in Awakening. I suppose the difference is that it training a super soldier or an uber powerful child unit is earned satisfaction, but grinding to max level on the first map isn't earned, just grinded out. For comparison, it's like using a normally weak Pokemon on your team versus grinding on rattata and pidgey until you crush Brock, and the rest of the game, with a level 100 charizard.
Actually Fire Emblem's core appeal is player expression through gameplay. Which units you use, which strategies you employ, which deaths you do or don't reset for, and basically any other decision you could make is perfectly valid and it's almost impossible to soft lock yourself by "playing wrong." No two people are going to have the exact same playthrough and even you wont have the same playthrough twice, not just because of RNG, but because there are countless decisions made throughout the course of a single turn, let alone the entire game and almost all remotely reasonable choices can lead to victory. LTC is just one form of that expression.