PoE is basically "classless"?

It's taken me a while to wrap my head around the skill/passives system that the game uses, but it seems to me that the only real class distinguishers are the player models? Any "class" can do any thing, they just may need to spend a few more passives to move from one section of the passive web to another. As a result, the power builds for each class look pretty much the same.

With every "class" able to use any item and any gem, all that really matters is the gear you wear, the number of slots that gear has and the choices you make regarding which gems to run, and which passives you go for. It makes for a very deep, complex, nuanced system, but leaves me with a question: Why have classes at all?

PoE is basically a classless system, without any class distinction. Or am I missing something?

certain classes are better at certain builds even if the difference is not astronomical.

It does add flavour.
Sure, you're relatively free to chose which path in the skilltree you want to follow, but that might result in you having to invest many travel points.
I mean, imagine a marauder summoner. You can do it, sure, but you'd have to go all the way up to templar starting point and then some to the right in order to reach Grave Consequences and other summoner stuff. Similar for a bow templar - the good bow nodes are between duelist and ranger.
But the beauty is - you can if you want to.

In my opinion, class specific items are not the way to go. I hated that in DIII and to some degree in DII LoD.

I understand why they've gone this way, and why they don't have class specific items etc. (which I've never been a fan of either; it's an entirely de-immersive, artificial contrivance - the exception to this was the D&D Cleric which had a character based ethical reason for not using edged weapons). Having such flexibility exponentially increases the number of builds and the depth of the system.

However, you lose any sort of meaningful class distinction beyond player model/animations/voices. So the classes themselves are pasted on visual flavour; facades. There is little meaningful gameplay difference (some due to the position they begin in the passive web, but as has been said not a great deal).

What the system gains in flexibility and complexity it loses in archetype, class distinction, and inter-class synergy. It's a numbers game, a power-gaming min/max spreadsheet. Seeing that has kind of taken the shine off it for me.

No need to defend against that, I realize it's the sort of system a significant number of people like. It's just removed one of the compelling reason to play these games - that of class playstyle, synchronicity with other classes, and a fondness for the fantasy of a particular archetype.

You can create dictinction for yourself and syncronicity with others through your build. Instead of picking something at the start of the game that says "you're like everyone else who clicked this button", you could pursue something such as using elemental melee weapons, and that would be your playstyle along with everyone else who chose that route. There isn't really a 'best' thing you can do, so it isn't just a min/max numbers game, you have plenty of options and playstyles available to you through what skills you use and what passives you pick.

However, classes are still there for many reasons: each character has a unique backstory, looks, as well as what quest rewards they get and where they start on the skill tree. While you can be a magic marauder, it's going to be a lot easier on you if you're a magic witch, especially if you're new. A witch will have more spell and spell-related skill gems given to them as quest rewards, and will have the magic passives in much closer proximity to their starting zone on the tree.

Would love one thing: each class has its own skill with lets say 20s-1minute cd. So they would be bit different apart from starting tree.

The more you build the better you'll be able to utilize the different class's distinctions. It can be fairly significant in the early to mid levels of a character. Late levels is when it doesn't matter quite as much.