ElDude has done a lot of studies based on player's age. Now, let me tell you something based on player's height.
From 1985 to 2017, of all the slams played only three were won by players 6'5" or taller (JMDP, Cilic and Krajicek).
That is three slams out of about 132 slams, leading to about 2.2% share. Zverev is 6'6".
Obviously taller guys have advantage in serve and in creating better angles. But, they also have several disadvantages.
They have trouble with movement. They have trouble with filling up and becoming stronger. They have trouble with
bending down on low balls. It remains to be seen as to whether these disadvantages can hold AZ back.
Hence, I don't think Zverev will become a multislam winner (say 3+ or better).
Also, while Sasha does everything fine, there is nothing that particularly stands out as his unique ability.
He is more or less like a generic basline player produced from a tennis player factory.
That's interestingly researched. I get your point about Zverev's height, but players are getting taller, and the one's that move well, like Zverev, do get looked at favorably. Safin is the original poster child for Big Man tennis. He was 6'4"/bordering on 6'5" and he moved really well. Everyone agrees, I think, that he underachieved with 2 Majors. That was his head, not his movement. (And a bit of injuries.) Zverev gets compared to Safin, and I think rightly. He's still light, and not filled out, but he moves so much better than some of the guys you think of who top 6'4". Men's tennis is getting taller, and I don't think his height will be to his detriment.
As to your last, I don't agree that he does nothing special. Serve, obviously, including 2nd, and a terrific 2hBh. He'll get better at the net, especially with his brother's help. As to how many Slams he wins, that's anyone's guess, but we'll all be shocked if he doesn't win any.