God, I really hope the next game isn't another sandbox emblem. Normally I would blame the customizability of every unit holding back some of the map quality, but then I remember that the Archanean remakes and Fates exist.
I hate how chapter 17 of both AM and VW is set up as something thematic but results in a rather mediocre map. Despite the actual win condition, the chapter is just a glorified rout map in an open field. It's all too reminiscent of bad Awakening maps which are never a good thing. I also hate that you're starting position is the same regardless of house. At least Fates had the decency to change the context of each route even if 1/3 of it was decent.
It's a little weird that gender locked classes are brought back in 3H considering it's a little more progressive than past titles.
I think only 3 houses is so bad because it is so free to just do whatever. Their are little to no real choices or restrictions, besides ones that make male units have worse class options from levels 10-20 till Wyvern shows up.
The last few games had customization, but they had strict limitations and costs to them (assuming you aren't grinding). Like you could make Corncob a Ninja in Conquest because Kaze has sketch strength and good 1-2 range was uncommon, but you had to suffer through E rank throwing weapons for a long while which is a problem. Same with making Selena a Pegasus where the only reason you don't jump from sword foot locked to flying lance locked is because of E rank lance in chapter 11. Second seals were also uncommon. It created diversity in player choice without removing character niches, Selena is one of my favorite units to use in Conquest because has a wide range of options she can go for. You can go Bow Knight to not cross class, Cavalier for the +3 damage on most terrain to fix her strength and use her sword rank instead of building a lance rank, or Pegasus to fly. You just had to make different choices and they had different trade offs and points where your decisions pay off.
Awakening has fairly limited class changing you get 2 whole other options one of which is usually shit anyway, like Archer Chrom, customization is not Awakening's problem. Awakening's problem is pair up is bat shit broken and some skills are just really really strong when paired alongside all those extra stats (like Sol). Galeforce is dumb, but you get that so damn late that it doesn't matter unless you purposefully want to break the game by grinding.
Customization by itself isn't the problem, completely unrestricted customization is the problem along with bad balancing. Conquest was a fairly solid game, ignoring the story and I still think pair up is bullshit I'll take gambits over pair up any day right now barring how broken stride is, so it isn't impossible to make a reasonable Fire Emblem with customization options. I personally think Fates had the best class change system it is reasonably limited so you can't just swap your entire army to different classes you could customize relationships to get specific options while still having limitations on what you do. Unlike 3 houses where "Just put everyone on a wyvern with a axe because axefaire, a lance if you have swift strikes, and a bow for 1-2 range and you're good" is a valid strategy for basically 80% of your army with the other 20% being casters or gambit carriers.
Is the new FE game worth buying a switch for it?
How big of a fan of Fire Emblem are you?
I'd consider, and most people I've seen that aren't total 3 houses stans, consider 3 houses to be on the average or maybe a above average game across the entirety of Fire Emblem. It has some cool mechanics and additions, but the maps are atrocious in a lot of spots and the story feels half finished despite having a lot of potential. The only people I've seen who say 3 houses is their favorite Fire Emblem are people who started really early with the series, or have some autistic obsession with one of the very divisive main characters characters. So it isn't an exceptional enough game to make owning a switch by itself worth it imo.
If you aren't an FE fan this may not convince you to be one as it is fairly anime for some people's tastes and the game isn't some technical marvel (kind of the opposite tbh). Fire Emblem as a strategy game is very fundamentals based for the lack of a better term, their aren't a ton of crazy over the top mechanics but because of that their aren't a lot of fancy things you can do that can take away from the basic fundamentals of a strategy game like moving, positioning units, and playing odds with hit rates and if you want to attack or not. Their are SRPGs with a lot more crazy bullshit then Fire Emblem has ever had, like FFTactics or Divinity Original Sin 2.