Hmm. I guess the best thing I like about Pokemon is probably the world. The variety of creatures that Pokemon has, just the prospect of in each game visiting and exploring a new region, meeting new Pokemon, and meeting and battling new characters is always a fun thing to do, and the biggest thing I look forward to in any Pokemon game. The world, really. It's the thing I will always like the most about Pokemon, no matter what flaws there are with each individual entry, the world of Pokemon in and of itself is thoroughly enticing.
Another thing, as green_typhlosion has pointed out, is features. There are so many little things to do afterwards that keep me playing and interacting with my Pokemon in various ways, or even outside of it. Contests in Hoenn and Sinnoh. The Battle Frontier in Platinum. Pokeathlon. Pokemon World Tournament. Mantine Surfing. Finding Pokemon in Ultra Space. Pokemon Amie in X and Y, and the three minigames that came with it (my god these minigames are so damn cute!!!). And in addition to battle facilities, also online multi battles. I love the battling aspect, whether it be in the facilities or with other players online. I love battling and what makes Pokemon battles so good imo is the variety of creative strategies I can come up with. The facilities or PvP allow me much room to come up with creative strategies and try them out, and that's fun. It matters not if it's Smogon or official metas like VGC and BSS. It's super fun. Because there's so many mons, many with unique playstyles, and you can use them in a team of six.
And that ties into the point of flexibility and creativity. Because there's so many mons out there, it's so much fun both in-game and competitive wise to try out new team compositions, and just have a blast experimenting with and exploring different Pokemon's capabilities every time.
I guess those are the big things I love most about Pokemon. Just the world, being in that world, and the battling part. Pokemon is not my favorite franchise, but it's like a comfort food I'm always willing to go back to. Just being able to explore the Pokemon world and engage in battles with many different Pokemon is a fun experience, even if the game itself may not be the best on its platform.
Compared to almost any other franchise Pokémon games have been a half-assed joke especially over the past 10 years. I think there's some understanding that we can't expect 900 Pokémon models to be as well animated as a Final Fantasy main character but Gamefreak's unwillingness to expand the games or try anything new in the main series has been a huge issue. Legends Arceus does seem to be trying to break away from the old formula which is neat, but if we ignore the appeal of Pokémon characters the game itself looks C+ at best. If Legends Arceus was being produced by an indie studio and wasn't Pokémon would any of you here give a shit? And if Legends Arceus ends up being a half-baked open world adventure with like 80 Pokémon I'd rather just play a fan rom hack, Pixelmon, or a non Pokémon game all together. Pokémon battles are fun but the franchise itself really has a "quality" problem that needs to be addressed. The Pokémon name will only sell games for so long until the reputation gets burned for good.
I think the biggest issue with Pokemon is that its formula has stayed stagnant, but said formula was always inherently unsustainable from the start and now the cracks in the foundation are beginning to show. Not to mention from a business standpoint it's grown far bigger than it ever should have. The formula was always "keep adding new mons and content to the franchise+everything from the previous games", but sticking to the basic Game Boy formula with more content tagged on was always going to be impossible past some point, and I think with SwSh that point has been reached. At the point of SwSh there was too much stuff to manage, too many mons, items, abilities, etc. and because of the way the franchise has become TPC commands strict deadlines so that became impossible to manage in such a short period of time. Not to mention there's a quick jump from going 2D to 3D and now going full console.
Game Freak refusing to let go of their control over the IP is also detrimental because it's clear that full blown console graphics are something they are not good at, and clearly from that standpoint things would be significantly better if they got someone else like Monolith or Koei Tecmo or whatever who have far more experience with console games to work on Pokemon. Game Freak's entire experience has been on dedicated portable consoles, and the GB, GBA, DS, and 3DS are all weaker than their home console contemporaries, but now the market has changed and the Switch is a totally different beast from past "handhelds". I point that out because they have actively shown that they can at most stick to weaker hardware: Red and Green worked well for something as simple and weak as the Game Boy, and subsequent entries were fine for their platforms, but GF having never worked with a dedicated home console before means that they have severely dragged themselves behind. Game Freak also has a problem with being stuck in the past. This is already apparent with how the gameplay has largely remained the same thus far, and how the games in terms of gameplay are still in many, many ways stuck in the early 2000s, but I firmly believe they do not realize how different a beast the Switch is from the Game Boy, DS, or 3DS. I think Sword and Shield and even to an extent Legends are being developed as if they were dedicated portable games, which sticks out like a sore thumb compared to the other experiences the Switch has delivered (and especially in terms of how much they cost compared to previous Pokemon games). I know you bring up Gen 6 as the peak and I agree with you, and I thought Gen 7 was fine for what it was (Sun and Moon+USUM were fun in terms of spicing things up in terms of in-game gameplay imo), but now with the Switch you can tell the cracks in the foundation are really beginning to show.
I think Pokemon as a franchise is long overdue for an overhaul of sorts, really. There's been too much legacy content piled up that is impossible to manage, the franchise has grown too big and from a business standpoint the old crunch schedule that TPC has put Game Freak through for the past 20 years is now severely detrimental to the games, and Game Freak refusing to loosen their grip on Pokemon games is also detrimental because they are now forcing themselves to make games on hardware and standards that are clearly beyond their own experience/capabilities, when really they should either seek assistance from a developer that has more experience in making console-level games or just let someone else take the reins of making Pokemon games, since the stakes are much higher now. It has stuck to tradition for far too long, and said tradition was always going to be unviable past some point, and now with SwSh it's clear that there needs to be serious changes to both the design formula and possibly the business practices behind it in general, possibly a corporate revamp in that regard too.