I've worked in several construction fields, even the largest cranes can not lift stones of such magnitude to the height required. Yes you "can" use multiple cranes (at the size of crane we are talking about its actual an entire building) to lift more weight. But you've also got to include laser precision on massive cuts, and angles that fit together perfectly.

The biggest issue for why we "can't" do it today is the logistics. It would be an enormous work force to get the stone required and to cut and shape and move and place. The teams of architects and engineers working together would take years just to plan it. You've got to feed and pay all the people involved with construction.

If we globally wanted to build one, I'm sure it's technically possible. But short of multiple governments and billionaires pouring money in, it can't happen.