Right, and all that makes sense, but then what’s the downside to classing up immediately? I’m a bit confused. It’s not like you lose levels somehow. Wouldn't it be better to have the benefits of better movement + stats right away at level 10 while you level up to 20+ rather than waiting until 20? That's 10 levels you're not getting any benefit? I feel like I'm missing something here
Historically, promoted units gain less exp unless they're killing other promoted units. Since promotion bonuses are static, if you don't need the boost right away you can take advantage being unpromoted to kill other unpromoted enemies to level faster. Additionally if the character in question already has good growths in a key stat you want to get to high values, those extra levels can go a long way.
Here's a few hypothetical situation
Scenario A: You promote a unit at the start of a battle that's level 10. They get the big stat boost (+2 all), they get a bunch of kills but only get 1 level where they get +1 str, +1 spd, +1 def. So your net here is +3 str/spd/def, +2 everything else.
Scenario B: You keep the unit unpromoted for the same battle, they get a bunch of kills and get 3 levels. The net of those levels is +3 str, +2 spd, +2 dex, +3 def, +2 luck. You then promote after the battle is over, your net stat gains are +5 str/def, +4 spd/dex/luck, +2 everything else.
Scenario C: Same as scenario B, however you get rng screwed, and your net levels are +1 str, +1 def, +1 spd, +1 luck and then you promote, you net +3 str/def/spd/luck and +2 everything else
In scenarios B and C the mission was more challenging because you didn't have the promoted unit with extra move, weapon types, and the big +2 all stat buff to start. Scenario A the mission was a lot easier, but your unit doesn't end up as beastly as it would have in Scenario B. Of course if you get the unlucky scenario C, you made the battle harder for a single extra point of luck which really wasn't worth it.
That's why it's hard to give advice on when to promote in FE. There's valid reasons to wait on promotions and valid reasons to promote right away. All of the above doesn't even take into consideration learning skills which starting in Awakening further complicated the "when to promote" discussion.
Edit: I didn't even process that your only experience was 3H where levels don't reset. 3H is a very different beast compared to all other FE games lol.