It's hard to imagine scaling this up to be able to throw a ton at a time.

If you want to throw something that heavy, you'll have a much easier time using explosives to do it -- and we've been able to do that for quite a long time now (multi-ton shells were fired in WWI).

Given the spin-up time and the fact it's a giant gyro (and thus can't be aimed) the ability of a 15" gun to fire payloads at enemy ships seems far more useful.