Coping
Ajax,
It is not correct to think that G/S Mini cannot "cope" with the situation.
The aim of the game is to prevent a situation where, due to sudden wind variations, the aircraft ends up at a speed that is too low for safe flight or with thrust fully at idle while speed is temporarily above command speed.
In the usual system, command speed on final is a steady value, and autothrust will chase that value.
If with the usual system, there is a sudden increase in headwind component, airspeed will instantaneously be (very) high and (auto)thrust will decrease rapidly, perhaps even to idle, which is undesired if it happens just before the flare (imagine that the wind decreases rapidly now, you will be on speed, but without thrust, engines will be very slow to spool up).
If with the usual system, there is a sudden drop in headwind component, airspeed will instantaneously be (too) low and even though (auto)thrust may increase rapidly, there is a chance of stalling.
The trick of G/S Mini is that it will VARY the COMMAND SPEED, to cut drastic thrust changes.
In case of a head gust, yes, the airspeed will increase, but so will the command speed, so thrust will not be pulled back. If now the gust dies down, you will be on speed, with the required thrust.
You are concerned about the situation of, say, 20 kts tailwind on final approach, changing to 5 kts headwind just prior to the flare (yes, such situations do exist in real life).
If you want to achieve the ideal Vref + 5 over the threshold, the only way is to "fly" the approach is at Vref - 20 (you will get the 25 kts increase just prior to the flare.
However, at Vref - 20, the aircraft does not fly anymore.
The G/S Mini idea to maintain Vref + 5 (minimum safe approach speed) is the best you can do in that situation. The resulting high airspeed over threshold is unavoidable. Remember though, that your groundspeed is not suddenly 25 kts higher! and groundspeed is what onground stopping is all about. Just don't let the extra airspeed prolong your flare, touch down at the required point.
Just think about the LH A-320 accident in Warsawa, a long time ago: they had 25 kts tailwind during approach, tower reported wind was about 10 kts from right front, exactly your scenario. Windshear was (of course) reported, so they (unfortunately) religiously applied the (then current) SOP: increase Vapp to Vref + 20. You can imagine the result over the threshold, there was a fatal overrun.
If G/S Mini had been available (and used) then the speed increase near the threshold would have been much less detrimental to safety.
If you properly think about this system, it will also be clear why you have to input reported steady state wind into the FMGC. The gusts are then taken care of by the variations in commanded approach speed , whereas in "normal systems" the steady approach command speed has to be increased, to make sure that variations around that command speed will stay above minimum safe approach speed (or stall speed, so you will).