"Fee" is a little misleading. It's essentially setting a pricing band where network/stakeholders benefit from the natural market making effect of selling at the high end and buying the the low end. If pumpers are persistent and push the price up to $1.06, then the conversion at $1.05 makes a profit; no one is paying a fee. Every day users don't need to do that, it just needs to exist as a function to the keep the price in the band. And it may not even happen that it gets used at all, at least after a while. As you say, nobody pumps HBD if there is a way to print a lot in a fast way, so this suffices. Someone may still try, but they won't keep trying.

This doesn't mean stability is limited to 5% either. It is similar to the status quo where if you know it can't stay below $1 then buying at $1 is a riskless bet, and even buying at $1.01 is pretty low risk. If the upper peg at 1.05 works then selling at 1.04 is likewise lower risk than buying there. Market forces should keep it away from the bounds of the band most of the time.