How is this game playable in melee?

If you have to acquire the pieces from an external source (trading and/or muling), just to play a style as basic and fundamental to ARPGs as 'melee', then I don't think a person can reasonably argue that 'melee in PoE is fine'.

Equally, if there is only one or two ways to play melee as your league starter and make their main character even without trading/muling, that is not 'fine'. A style as basic as melee in a game with this many active melee skills should not be limited to a few skills from scratch. Especially not when the game gives the vast majority of those 'maybe not so viable active melee skills' as quest rewards.

Totems I don't consider melee. They're just at-range skills that might deal melee damage themselves. They're summons, in typical ARPG terminology.

And of course, if you're just using your melee weapon as a focus for ranged attacks, then no, that's not melee. Attack waves, projected slashes, blah blah blah...not melee. Ground slam, Sunder, and Lacerate, all of which have 'wave' in their descriptions, can gtfo. None of those skills requires you to actually hit an enemy with your weapon. Not melee. This goes for any other 'melee' skill that follows the same criterion.

Cleave has always been borderline for me because for a while there it was sort of more like the basic attack from the classic sega run-and-slasher Strider than anything and that's never cool. And Reave, something similar. So Rule of Cool overrides here.

I'm also a little less strict on the notion of the pseudo-melee of spell-triggering. In an ideal ARPG, melee would absolutely mean hit things with weapon -- do damage with weapon -- things go splat. But for a long time, hybrids like 'spellblades' have been a thing, and proccing spells with melee attacks can still be considered melee. This is one of the primary ways to approach melee in a game like Grim Dawn, which for me is all about proccing decent sized AoE effects on attack as a Blademaster. Similarly, I loved Cast On Critical Strike in PoE from the start, but it is not what I'd consider a primary melee style. I had to sacrifice a few gem slots, spec into all sorts of passives, and generally 'bend' around the game just to make something cool. But if a person can make that or any other 'melee-triggered' build work, eh, they're still getting into relatively close quarters combat with their character. Still melee, I think. Melee-adjacent, at worst.

'Strikes' that require you to hit a single target before unleashing secondary effects are melee. Lightning Strike has also always sort of baffled me and embodies GGG's early inability to clarify skill categories. The projectiles cannot miss IF you use it as a melee skill, and the projectiles deal less damage than the initial strike. But you can just sit back and spam the bolts if you want (it's almost never been a good option compared to actually casting), so I'm inclined to throw Lightning Strike out of the melee club.

Vaal versions are 'super' attacks and should be granted much more leeway as regards range and efficacy. A Vaal melee attack that suddenly behaves like a ranged AoE is perfectly fine.

I'm sure I've missed something. Probably lots of somethings. It wasn't my intent to run down all of the melee tagged skills in PoE like Conan The Librarian, only to use a few of them as examples of what I find contentious in PoE's existing 'melee' category.