Being perfectly frank, I find the "slot-filling" complaint to be rather flawed. The only classes most folks can point to which even remotely meet that definition are, as far as I can tell:
Avenger
Invoker
Battlemind
And of those, only the Battlemind is even remotely lacking, because both Avenger and Invoker have some solid lore and clear mechanical niches.
I will, however, grant that Battlemind is a stupid name. But still, 1-2 rough fit classes out of 25 is not even slightly deserving of the hand-wringing and accusations 4e received on this front.
Okay so...how would one fix that?
Because I am never going to accept a game design that leaves characters with nothing constructive to do. The game needs to provide a solid starting foundation, a core that consistently works. The 5e Fighter fails on the "works" part, while the Wizard fails on the "consistently" part (that is, as mentioned up thread, a poorly-built Wizard is actually kind of weak, while a well-built one is one of the most powerful characters you can play in 5e.)
So... where's the fix? What can we do that actually delivers consistently functional, effective characters while giving people this mysterious je ne said quoi that will appeal to more people?
I'm just going to say that there were several classes I didn't like in 4e. I didn't like the Rogue, for example, as so much hinged on getting combat advantage, and sometimes you can't always count on flanking or a friendly daze. You needed to generate that yourself.
I didn't care for the Warlock, because it had a funky design, and didn't seem to understand what it was supposed to be doing as a class. Was it a controller? A striker? Some hybrid of both?
I didn't like the Paladin, initially, because their mark punishment lacked bite, and until Divine Sanction was added as a mechanic, couldn't multi-mark.
I found the Monk too fiddly, the Sorcerer underpowered, the Swordmage was a hot mess, the Battlemind didn't have a melee basic attack, the Ardent was trying to reinvent the wheel (badly, IMO), the Psion had a neat concept, but it didn't stand out enough from the Wizard, the Assassin was designed with back loaded damage, which felt just bizarre for it's role (the premier alpha striker). The Seeker needed more options, and too many people were building it to be a damage class, which struck me as rather bizarre.
Even though most of the classes had a similar framework for their powers (AEDU), the power level of those abilities was often inconsistent, PHB1 classes got more support, and some of the classes were designed strangely, as if someone said "hey, we need three new classes for this book, throw something together over the weekend, ok?".
I loved playing 4e, but not all of the options were created equally. Like, ok, I can forgive PHB1 missteps, like not well defining the controller role, but by the time we're seeing things like Martial Power 2, you think it would be understood that each role requires a specific kit to function.
Defenders need melee control effects, and ways to deter even tough foes from deciding to violate your mark. They need to be able to make opportunity attacks, and better withstand taking a beating from foes.
Leaders need "oh carp!" buttons, non-trivial buffs for allies, and the ability to set up favorable attacks and get allies out of danger.
Strikers need to be able to burst down regular enemies quickly in a pinch, and have powers to get them into (and out of) striking range.
Controllers need to be able to lock down foes for multiple turns, or affect large groups of enemies in the short term.
Too often, I'd look at a new class and wonder if the designer forgot what role they were trying to fill.