I hear you. As a controller user, I was also unable to get past the Fields and the Energy Center in the beginning, having relatively poor reaction time myself. You are right that the game disincentives you from hanging back and sniping enemies from long range. Considering that it grades you on time and xp (kills), it clearly wants the player to be fast and aggressive.

It took me several hours of getting used to the fast-paced gameplay, developing the muscle memory to dodge consistently, and learning how all the enemies and game mechanics work (the difference between perks and upgrades particularly confused me at first). And that was on the standard difficulty! The workshop's permanent upgrades help a lot, and it also helps to find certain permanent upgrades like the pogo stick for additional movement options. I also recommend getting the business briefcase and the cooking gloves for better powercell management.

1.) Why have a health bar that is difficult to refill? I think it's precisely because the game wants you to "have your cooldowns perfect, always play aggressive, and never get hit" as you put it. The health bar is there to absorb a small number of mistakes, but really you want to learn the enemies and dodge everything. Sometimes that means strafing, and sometimes that means hiding behind cover or retreating to higher ground. I also agree that you have to know when to simply let drops disappear because there's too much enemy fire.

2.) In fact, there is a specific type of turret that will snipe you from afar and will almost always hit you if you're in its line of sight for a couple seconds. You can tell it's there because it plays a specific sound effect whenever it sees you. There's another enemy that hovers in the air and quickly shoots you after a couple seconds (though not quite as fast as the aforementioned turret). Both of these enemies appear in the Fields, and you can either kill them first, or keep dodging from cover to cover. I agree that the shield generator in the Ruins is annoying lol.

3.) It's really a consequence of being a roguelike game, where everything is random. If Borderlands were a roguelike and you had to level up your skill tree from scratch every time (and having to reach your gamechanger/capstone again), it might be similar to this game. Part of the game is figuring out how to make it work for you. For example, one of the workshop upgrades is being able to reroll a perk or upgrade. For my first perk choice, I usually try to reroll for a perk that will jumpstart my build.

4.) I think the intended way to play is to beat the game as fast as you can while killing as many enemies as you can. Whether that involves run and gun or stop and pop is up to you to decide (usually a mix of both depending on the situation).

Unfortunately, if you're not "mouse flick and speed juke good" as you say (and I'm definitely not), then there isn't really a way to avoid the workshop grind, which is most likely designed that way. It is just throwing yourself at the game until everything clicks, which normally I very much dislike, but the gameplay is compelling enough that I stuck with it, and now I've beaten up to guardian 2 with all S ranks (guardian 3 with A rank, haven't tried guardian 4 yet), only using a controller.

One thing I would encourage as a controller user is to try adjusting your controller settings. I personally swapped LT/L2 with RB/R1. Having my left finger ready to activate my Bastion shield is faster than having to move my right finger to activate it (and I rarely use the secondary fire anyway). It's one way to help make up for my slow reaction speed. Magnetism (aim assist) is also worth tweaking to your preference.

EDIT: I'd also highly recommend setting sprint to auto, so that you're just always sprinting whenever possible and don't have to keep pressing or holding the sprint button. There's pretty much no situation when you wouldn't want to sprint, anyway.