Discussion: which game had the best balancing overall?

By balancing, I mean:
- Wild Pokémon available for capture (not too overpowered, not too wimpy)
- Evolution methods available at key parts of the story (broken 'mon to make a gym battle overly simple)
- Wild Pokémon's levels and movesets (or as I like to call it: how long one has to suffer horrid wild Pokémon training)
- Level and difficulty leaps or lack thereof (I've heard gen 5 has an awful leap for post-game)
- Moveset distributions relative to the game's story

I'm asking because I think that would also make an interesting discussion in the romhacking and fangame base.

For me personally, when considering your listed points: Alola. I think it had a wide range of available Pokémon and few difficulties with evolution that I could remember. I really enjoyed going through the game and having so many different team members to choose from. Am sure I'm forgetting certain flaws with Alolan game balancing, but I still enjoyed them a lot overall.

RSE are others I find to be decently balanced for the most part! Training for extra levels wasn't massively necessary for me, and the trainers had Pokémon that gave pretty good exp most of the time.

can't truly answer. i think each game till gen 6 (excluded) were somewhat balanced. In some games u had to grind a bit, but it truly depends on experience. i think that from gen 6 games everything got easier tho, with gen 8 being a gen where it's almost impossible to loose. But again, I wouldn't say there's a perfectly balanced game. They all kinda aren't from my experience

I'm going to say gen 4. Maybe it was just my experience with it at the time and the wicked nostalgia trip of returning to Pokémon after so many years, but it just felt really satisfying to me.

I've only played Gen III-V (and barely remember B2W2). If I can narrow the criteria down to only cover up until the first Champion battle (or N in BW) then I think Unova in Black and White has the best balancing according to OP's criteria. Because its so prescriptive in the path you follow, it can be designed to maintain a steady progression. I feel like it has one of the better varieties of types early on too. Giving the evolutionary stones so early on for the elemental monkeys does handicap you somewhat by leaving them reliant on TMs from below lv. 20.
Kanto and Johto have one of the worst level curves, but its because there is so much freedom in how you play the game. In both cases around 1/3 of the region opens up once you have 3 gym badges - in Kanto you can defeat Team Rocket in Silph Co. whilst having Lt. Surge as your most recent gym win iirc, whilst in Johto although you need Surf to actually fight any of the gym leaders after Morty, you could travel all the routes between Olivine City and Lake of Rage once you beat Whitney. This freedom only works because they keep the levels roughly consistent along these routes. But you then end up with a leap -particularly in Johto when you go to take on Team Rocket and then Clair, then a further one to the Elite Four because the wild Pokémon levels post-Blackthorn are miserable.

I don't really have an opinion over which way is better.

The most balanced games are for less those of Hoenn, Sinnoh and Unova. (The originals, not the remakes with the Exp All which multiplies experience gains by a factor of 4 with a full party).
Since the 6th generation, it has become almost impossible to lose.
However, the latest games have an important point: QoL. Before Unova, learning skills was frustrating. Unova transitioned to Unlimited TMs, then Kalos allowed Pokémon to keep their moves history.

I'd like to point to Generation V, especially B2W2, since I've played B2 most recently. Unlike some older games (cough OG Johto, Hoenn and DP Sinnoh cough), you don't need to worry about finding usable Fire-types if you didn't pick Tepig as your starter (yes it ticks me off a lot when one starter type isn't as available as the others). The regional dex itself is pretty well balanced and allows for some pretty unique team compositions (especially when, in BW, you have only about 60 evolutionary lines to work with if you can't trade), and Set Mode provides a decent enough challenge. Plus, if you'd like to play just a teensy bit riskier in routes, there's dark grass. Grinding doesn't need to be an absolute chore either, since Audino are everywhere to help level you up (not too much, since the new leveling system makes overleveling harder). Gym Leaders, Elite Four, and the Champion even use held items on their Pokémon, to make things a little harder.

If there are any major gripes I have with them balance-wise, though, I will say that some Pokémon evolve way too late (the usual culprits Rufflet, Vullaby, Zweilous, and Larvesta). This isn't an issue exclusive to Unova, but there are some Pokémon that simply aren't worth the trouble of getting (why can't I even use Heatmor until Victory Road or B2W2's postgame, when I most likely already have Emboar, Darmanitan, or Chandelure on my team?), and basically everyone who's played B2W2 (except me) has used a Lucario on their main-game team, so if you want to give every Pokémon in your dex a chance to shine, you'll need to balance availability and usability with some elegance.

As for moveset distributions, I don't think about those very often, but from what I've experienced Generation V is at least decent at it. I'm not getting access to truly amazing moves until much later in the game, but the reusable TMs make it so that teambuilding isn't that much of a headache.

perhaps gens 5 (specifically BW) through 7. audino make for a good exp source so I never spent too long to train for the next battle (although I hadn't completed the postgame). XY and ORAS were pretty linear, apart from a little jump between defeating the bad team and the league. in SM the only real trouble I had was Kukui's Snorlax. some trials were more challenging than others, but it was always possible to handpick useful team members for every task.