I do agree that the client should warn the player, but to be fair, comparing this situation to dodges on knockdown is not quite accurate because the ability is, technically, working.
For example, imagine if this were to happen:
is hit by Chillbane. Next turn, reveals a 2 attack and reveals a 4 attack. If does nothing, then 's 4 attack out-speeds because 's 2 attack is 4.4 speed after Chillbane. But, if uses BoS, then her 2 attack speed is first reduced to 1.0 and then raised to 3.0 by Chillbane. Now out-speeds and wins combat.
This is not a likely scenario, perhaps, but it is theoretically possible.
I think the better comparison to be made here is to DeGrey's 7*. If you combat reveal the 7* and the revealed side wins combat, and then you try to discard and rotate, the game asks, "You're already winning combat. Are you sure you want to rotate?" Because of that kind of precedent, arguably it is reasonable to assume that the game would similarly say something like, "You will still lose combat after using Burst of Speed. Are you sure you want to use it?"