My problem with TPS was the same as you described, ie loot being useless too soon and generally feeling unrewarded for playing when the playing itself felt like a grind. I hate spongy enemies in FPS games and TPS enemies were like that, especially the bosses. IIRC I quit the game the first time after reaching that female commander in a mech bossfight due to her being spongy and me running out of health and ammo. I then tried again a few months / year later and quit at the same place for the same reasons. The electric and burn damage some enemies could do seemed unfair too. I really liked the aerial aspect though, wish they would've done more with it.
In your opinion, is it possible in BL1 to play as a melee or stealth character? In BL2 there's a class for that I believe but if its like you mentioned, I wouldn't like it. TPS isn't good for melee though, despite me playing the melee character. Too little damage.
You were pretty close to the end then. There are only 2 bigger areas after that before the end (excluding the DLC). And yeah, the DoT damage the enemies do is one of the most annoying things in the game as it deals massive damage and there are not many counters to it.
Playing pure melee in BL games is quite annoying at best, because from BL 2 on, there are so called "roid" shields, which boost your melee damage when depleted. In order to play pure melee, you HAVE to use a roid shield AND you have to find a way to deplete it before starting a fight and keep it depleted. Extremely annoying and tedious thing to manage which also makes you pretty fragile. And without roid shields, melee only is simply not viable.
But I greatly enjoyed the hybrid playstyle of Athena in TPS. She has a melee tree that was great fun and supports a playstyle, where you hit enemies with both melee and ranged attacks from close range and works great even without roid shields. Combined with her action skill, it was by far the most fun I've had in Borderlands.
In BL 1, Brick could probably be played as mostly melee, although I'm not sure as Brick is the character I almost haven't played.