Just because you're invisible doesn't mean you're hidden. In exactly the same manner as an invisible Paladin clanking down the hallway, everyone knows exactly where everyone is within the darkness, unless they take an action to hide and win that stealth check; and even then, you're only hidden until you do something interesting, at which point you've revealed your location.
If there's any other melee in your party, then they'll be at disadvantage on their own attacks - unless it's a reckless Barbarian, who can overcome the disadvantage of Darkness by giving enemies advantage against themself. If there's no other melee in your party, then the monsters will just leave the darkness and go engage someone else.
The Darkness trick is a powerful defensive ability, but it's not a tank ability because it doesn't put the Warlock into that role. If doesn't give the monsters any reason to actually attack the Warlock instead of focusing on someone else.
This.
Although darkness (and invisibility) does stop you being targetted by most spells, many special attacks and attacks of opportunity.
For example, an invisible creature (or one standing inside darkness) is immune to Power Word Kill regardless of if it's also hidden or not. The spell can only be cast on 'Choose one target that you can see...' like most offensive spells in the PHB.
Can you maintain concentration through a short rest?
Absolutely you can. And starting at Warlock 5, Hex lasts 8 hours long.
You cast it as a bonus action on the first turn of your first encounter of the day and it lasts all day long, until you either lose consciouness, cease concentration willingly, or fail a concentration save.
So for a 'standard' Fiend Warlock of levels 2-10 it goes (on a standard adventuring day/ dungeon crawl):
Encounter 1: Cast Hex. Spam EB and invcocations
Encounter 2: Maintain concentration on Hex. Cast 1 spell at max level. Spam EB and invcocations
[short rest] - recover slots, spend HD
Encounter 3: Maintain concentration on Hex. Cast 1 spell at max level. Spam EB and invcocations
Encounter 4: Maintain concentration on Hex. Cast 1 spell at max level. Spam EB and invcocations
[short rest] - recover slots, spend HD
Encounter 5: Maintain concentration on Hex. Cast 1 spell at max level. Spam EB and invcocations
Encounter 6: Maintain concentration on Hex. Cast 1 spell at max level. Spam EB and invcocations
[klong rest]: Restore HP to full, recover 1/2 HD, recover slots, Hex drops.
Compare the above to a Wizard 2-10 over the same adventuring day.
There is nothing wrong with the Warlock, and the OP's argument is based on subjective experience.
As long as the DM is policiing the 5 minute adventuring day, and giving the recommended 2-3 short rests per long rest,
the classes are balanced fine against each other.
So OP: Its not the Warlocks fault. Its your DM's fault. Tell him to do his job and stop being lazy.