Ultimately I think the fee should apply on both sides. With the fee only on the high end, HBD will tend to trade in a range of $1-$1.05, which isn't really desired. Better with the same total fee would be for it to trade in a range of 0.975-1.025, which hopefully would tend toward stabilizing around $1 (vs. $1.025 with the 1-1.05 range).
I agree with your point that this isn't critical so we can ignore it for now in order to simplify implementation. If we end up with stability in a range of $1-1.05 that would be a short term great outcome we could then refine later.