How are L2’s cheaper?

I had written a bunch to try to ask this question. However, no matter how many times I tried to structure the question it always turned out quite wordy. So, I've deleted everything and will try to ask with one sentence and see where the conversation evolves from there.

If all of the sudden everybody using ETH for transactions used let's say the polygon network wouldn't the fees on the polygon network then all of a sudden become crazy?