In the past I've described the problem with Pikmin 2's caves as jury-rigging a resource management game onto a time management game. Nothing about Pikmin's gameplay is particularly geared towards this. The Pikmin are a resource you need to be mindful of, but only because poor use of them costs time, which is truly finite and valuable.
In 1 you have infinite Pikmin so long as you have enough time, and in 2 you have infinite time so long as you have enough Pikmin. The caves are defined by the fact that they limit you only to what you brought in with you. This makes them inclined to be endurance challenges with the goal of killing you outright, rather than concentrating the difficulty more in proper planning to overcome obstacles efficiently, and so the cave meta just naturally becomes leaving your Pikmin at the start of the sublevel and running around punching everything to death and triggering all the traps you can before even thinking about putting your squad in harm's way. This, of course, is not fun.
Cheap as these mystery dungeon-ass levels were, they did do one very important thing for Pikmin back then. It's important to remember that for a very long time, Pikmin 2 was by far the largest Pikmin game, and it was the only one to have the Piklopedia. It's the game that gave Pikmin a whole fleshed out world and let you take the time to really appreciate it, and the change in structure and focus is why. The reduction in scope is possibly the single most common complaint with 3, but there's only so long you can reasonably make a game with a hard time limit meant to be replayed and perfected.
4 identified the need to compromise on this front if Pikmin games were ever to be any bigger, but was probably too uncreative about it. Giving caves actual level design and at least paying lip service to the idea of time passing helps, but I'm not sure why the concept was brought back at all besides it being the only precedent we had for a larger Pikmin game. Now that they require bespoke level design, it's difficult to say what is actually being gained from this approach specifically over just having more areas to explore. The cave sublevels are sort of more focused challenges than the overworld offers, but that mostly just means they resemble traditional Pikmin levels a bit more than a lot of the kind of aimless overworld areas in this one. I can't tell if that was a purposeful division or not, but if it was, no thanks.
I would have preferred something that played into the time mechanics rather than bringing back something designed to sidestep them (it still kind of does, if you enter just before sunset time won't pass at all). By all means, have a game with infinite days again, but give more specific time goals to reach. Have changing weather, changing seasons, migrational patterns, something like that. Things to instill a sense of urgency or satisfaction upon reaching a self-imposed goal, cyclical things you can punish a player for missing without just resorting to a game over. Might have said it before, but kind of like the famous "imagine a bus" Mario speedrun analogy.
Instead of caves, have smaller areas like past games and 5-10 more of them, or have 5 or so much larger areas with multiple landing sites to discover. Not for the purpose of constantly moving your base around to be closer to the action like in this game, but because the area is so huge you need to be able to choose where to work from.
Are there any other games like Pikmin, specifically like Pikmin 1? Maybe some unknown indie game?
In addition to the ones already mentioned, there's also the old cult classic Wii game Little King's Story, which is available on Steam these days. I can't say which specific Pikmin game it might resemble most, but I have played a bit of it in the past and definitely remember it hitting a similar vibe of cutesy yet very weird and slightly dark/unsettling. Instead of Pikmin, you order around a mob of your citizens and give them different jobs as they work and fight and die for you, which is kind of saying the quiet part out loud.
Hope this is a DKC Returns situation and Mercury Stream redeem themselves with the next one (if they're in fact working on it) like Tropical Freeze did
(Yes, this post is just an excuse to post awesome Metroid music).
Ironically, all of those Metroid tracks are from the DKC Returns composer.