Problems that exist mostly in your mind - and not the minds of the plurality of people that have made the warlock the single most popular casting class in 5e. Why must everything be blended and homogenised to your precise tastes? Why can't you accept that a plurality of spellcaster players like the warlock the way it is? Given that the warlock is observably the most popular spellcaster (no matter what the table surrounding you personally does) pretty clearly if the warlock being an outlier is a problem the answer is that we need more classes that work in similar ways.It would put an end to multiclass abuses. It does little to fix other problems. But at the very least it's a band-aid.
The warlock is the simplest and most newbie friendly spellcaster both to make and to create from scratch. The only time it isn't the simplest is that you level up many of your spells on level up (rather than deciding which level to cast spells at). The only people who find it hard are those who've been playing D&D since before 5e was launched and who also didn't like 4e.
It is also in some ways the most magically potent caster at both the high and low times. At high moments it has two (or more) spell slots that are as potent as the best slots any of the full casters get - and they don't get to get them back on a short rest. 1st, 2nd, and 6th levels are the only times when a warlock doesn't have the same high level nova potential as a wizard. And its actively better at 7th, 9th, 11th, and 12th. Meanwhile at the low end of the spectrum an Eldritch Blast backed with Agonizing Blast at 5th level (assuming charisma 18) is a match for the second level Firebolt spell (slightly less damage until you hit Cha 20 - but Force > Fire). But you also get Invocations - which can be at will spells. The ability to cast Silent Image or Disguise Self as at will spells really pushes them to the next level and lets you use specialist illusionist style shenanigans. You also get your pact boon - making you potentially either the best ritualist in the game or giving you a flying, intelligent scout. In exchange they lack the mid-level slots which are highly useful.
The warlock's lack of spells known is nowhere near the problem it is for the sorcerer. The sorcerer (up to level 11) only knows a single spell more than the warlock - but they have to spread those spells over multiple spell levels so they don't end up wasting those lower level slots.
The only significant problem the warlock has is the hour long short rests issue. And Tasha's has pointed out an obvious way of fixing that - you recover your spell slots on a 5 minute ritual you can use proficiency times per day. There are trivial issues involving multiclassing, the first of which is that Eldritch Blast should be a class feature that scales with your warlock level not your character level and the second is that the Hexblade is a patch for Pact of the Blade being bad; it's fine for a warlock but broken on a paladin; the fix involves fixing the pact of the blade (charisma to attacks - but extra attack only on warlock levels) then dropping the hexblade. (And yes there are a whole lot of bad invocations that should be dropped from the game and replaced with good ones, including all the ones that give you an extra spell you can cast with a warlock slot).