Well, here's the thing about boiling with a 4500W element. If you opt not to use a PID and SSR or some other method of controlling the power output of the element, you're going to have quite the violent boil going on. You'll end up wasting energy and boiling off a lot more than you would expect. I guess if you can figure out a way to reduce the power of the element once you reach boil, then you should, theoretically, be able to do what you're thinking.
If brewers use a PID on their boil kettle, they're using it in manual mode and then limiting the output percentage of the PID rather than using it in PID mode. (That won't work well once the boil temp is reached)