It would cost "nothing" to mount an attack because the attack mining is profitable for other reasons.

Say instead of hashes it was computation cycles, so long as your computer is doing something then it counted. (I am ignoring the bookkeeping problems)

I could take a supercomputer that I am using otherwise for economic benefit, and perform a whole bunch of mining with it, at no cost to me.

Even better, I can go to several supercomputers and do this, all without costing any actual computation power.

This would allow me to create a ton of power on the network, which could be used to overtake it and break the usual security guarantees.

However with Bitcoin I have to stop doing anything else with all of this computing power, which is a problem.