Say the level cap didn't exist or was 1000 instead

how much harder/easier do you think Pokemon would be if no level cap existed? Or say the cap was higher, like, level 1000.

It wouldn't be any easier or harder, just substantially more time-consuming. Said it before and I'm sure I will say it many times again, but just because something takes you longer to do does not mean it is harder to do. I imagine the EXP growth rate would be substantially more, or there would be more ways to get around the levelling process - or levels might not matter at all - but I can't imagine it making a huge amount of difference. If it was removed entirely then I imagine stat growth would be more important - think candies from Let's Go/Gummis from PMD - and that the type chart would be ramped up to eleven to compensate.

...although the thought of Pokemon with Disgaea's level of grind is both amusing and terrifying to think about, because Pokemon's gameplay loop is significantly more basic, so I can't imagine it being quite as much fun or anywhere near as satisfying.

I'm not sure if I can answer for certain easy or harder.

I can be certain that YouTubers would be grinding to level 1,000 before the first gym.

It would depend on how they impliment it.
If they just increased the level cap to say 255, or 1000, and didn't change anything else then the only difference is if you continued to play the game you could eventually make a basically indestructable pokemon when it comes to wild pokemon/trainers.
If they increased the level cap and also balanced the rest of the game around it, be it having higher level pokemon or gaining more EXP then it wouldn't change the game much at all imo. Maybe it would make it hella grindy if they just made other pokemon higher levels than they already were.

I think the only way increasing the level cap could improve the game series is if they used it to include more content. Imagine if they had so much post game content that wild pokemon ended up being levels 100+

Past 100.... we'd definitely be given a lot more exp items (like the candies in SwSh). Goodness I cannot imagine Pokémon being that grindy without items to boost it more easily lol. Agree that the only good way, imo, for the cap to increase is to add more content. If they just scaled experience differently and changed the cap so not much ultimately changes, then it'd essentially be the same as having it as 100 anyway.

it'll just be really boring. getting to 100 like... pre 7th gen was kind of an annoying chore as it is and there isn't even anything special about achieving that beyond learning everything in a given pokemon's set + maybe for battle reasons.

When you increase the level cap you also need to adjust the leveling curve. Either by making Pokemon level up faster or by providing better means of dealing with those now even higher leveled threats. Alternatively, if we took a similar approach to the games as was done in the Disgaea series (max level cap 9999), then the main story would still play out as normal and anything beyond level 100 is postgame. At that point, taking into account that most postgame challenges (online or not) use level scaling, it kind of makes a higher level cap kinda pointless.

To account for the increased level cap, the games actually need to provide more challenges that need to be solved by grinding. Legendaries that are way too high in levels, that just stomp on your party unless you grind your way up and stuff like that.

Honestly, I could see them sooner doing away with levels altogether than raising the level cap. It just seems way to troublesome in terms of balancing. And we all know how good GF is when it comes to stuff like that.

Competitive pokemon would EXPlode (see what i did there?) and people would spend days at a time training a Tyranitar up to like level 500 and stuff.