Some days it won't make a difference because the stabilizer, even with the previous, larger, proposal does nothing and just sends most or all of the funding back.
Other days, when there is more imbalance, it may deviate more from the peg. If it looks like more funding is needed that would be all the more reason for someone else to make another proposal, though I think this is a good idea for robustness in any case.
RE: HBD stabilizer evolution May 2023