You have to power it all the time, but the amount of power it uses while it’s on will change by up to a few orders of magnitude depending on the gpu. It’s not uncommon for a gpu to be pulling just a couple of watts at idles and several hundred at full tilt.

So the only way it’s a fixed cost is if you don’t pay for power. If you only consider the cost of the power, it might still be cheaper paying for an api.