Why 'Stops' for exposure?

It's still in use because:

It has caught on pretty firmly

The true values ALWAYS differ slightly, so precision would be wasted

You can't set numbers precisely with an analog controller (re: Sony example)

Such fine adjustment isn't needed. You have 1/3 stops in-camera controls and 0.01 stops in-software. Which again begs the question, why isn't it implemented. I think it's because it would be too much of a hassle (imagine deciding between ISO 582 and 583)

So, for one answer, I'd choose the last one over the others.