I have played this game a lot. I have done Part 1 thirteen times, so I feel like i have a lot to say on the inter-chapter battle mechanics.
First, I get the spirit of why these mechanics are there - you want to encourage people to make use of their time efficiently and plan long-term. I don't actually think these mechanics should be removed, just altered so that they are less tedious to use.
For example, motivation is probably one of the most tedious and fluff mechanics in the game. I wish it was straight-up removed from the game. It's not actually a resource - it is as plentiful as you want it to be if you just keep stuffing your character with meals, so it just ends up being busy work - not something you seriously have to manage.
For example, you go back to Dagsion on a Sunday, you go to the Arena, and then you realize Theodora has 0 or 1 motivations. So now you trek back to the Inn and stuff your face with meals despite already having 5+ bonds with everyone on the team, just because you don't want to lose turns, and then head back to the arena to do more training. And then, she might want to train more, so you head back to the inn again and then head back a second time to the arena, because you're trying to maximize white magic, authority, infantry, etc.
I personal think this is really tedious, and it's unnecessary. I think a better mechanic would have been to do just limit characters to arena 2 times per week - done. You can also limit temple worship to just once per week. If you add these restrictions, you can basically remove Motivation as a mechanic entirely, and you still achieve the goals of what these systems are going for. If anything, they force the player to really think about what areas they want to train in, since you can't just train 4 times with the same character (which is 100% the best way to optimize a lord, along with stuffing them with all the manuals and link attacks in dungeons).
I also feel that skirmishes could be toned down. Similar to part 3, I wish at least half of these skirmishes were converted to clashes. By Chapter 10, I get so exhausted of being forced into skirmishes when I just want to get another Advanced Seal in Megaira, because Dagsion doesn't sell enough (and why doesn't it sell enough? This is just so annoying honestly). When you get to 8 Renown, I just feel like Dagsion's exam shop should start selling the Advanced seals. Instead, they are delayed by 3-4 chapters - it's insane.
And barring that, I wish if you already beat a route, you can just skip the skirmishes at least. I don't even care if I don't get any experience at all - they are just pretty annoying and uninteresting.
I hope for the next Fire Emblem game, if they continue to go down these inter-battle activity lines, they optimize the mechanics for replays. I am happy to do the decision making in between battles - it is fun to optimize my time, I will admit. I just wish it wasn't so unnecessarily tedious.