Just in case it’s not fully clear, the cost to run services (i.e., canisters) is measured in cycles, which are already tied to a basket of fiat currencies. Only ICP ledger transaction have a fee in ICP.
As I mentioned before, and @bjoernek agrees, I don’t think this change would have a tremendous impact on the burn rate.
However, this proposal has some appeal: In the current model, if the ICP price drops, the cost to run a denial-of-service attack goes down as well. Keeping the transaction fee fixed in fiat terms would mitigate this risk.
I’m not sure if this security concern is reason enough to change the current mechanism, though.