Higher structural costs presumably. In the idea presented here you only need to move a small amount of mass at a time, so you don't need an especially strong crane.
If the giant block was literally just suspended and a crane would hoist it up and lower it to recover energy. Then this would put continuous stress on the crane structure. Much higher than a series of smaller blocks being lifted intermittently.
I was thinking the same but with chains or some heavy contiguous body. The problem is that you need something that can lift one super heavy load, as opposed to many lighter weight ones. I guess that's what you mean by hydraulics but then you need hydraulics