I don't see a practical problem with very heavy monolithic blocks. Over a century ago, people built perfectly stable hydraulically-powered draw bridges that have opened and closed several times per day, every day, up to the present. Sounds like a solved problem to me.
You're orders of magnitude off on the scale involved.
A single one of these concrete blocks is 35 tonnes. To get useful stored energy levels you need thousands of blocks. So you're looking at something like 100 kilotonnes of total mass. That's way, way, way more than any movable bridge weighs. Bagger 288, the largest mobile machine ever built, only weighs 13.5 kilotonnes, and all of that weight is supported by the ground on massive treads. To be able to lift many times the weight of Bagger 288 over 100 m in the air defies imagination as to what would be required. It would require billions of dollars to achieve, most likely.
Contrast with an off-the-shelf tower crane that costs a few million.
Are you sure those bridges aren't counter-weighted? I don't believe I've ever seen a drawbridge that wasn't.
Moving a counter-weighted something-heavy up and down is a distinctly different physics problem (that closely resembles moving it back and forth horizontally) than moving an unattached something-heavy up and down.
