From your question, it seems that you have the following situation:

An aircraft is having a constant angle w.r.t. the runway to compensate for a crosswind. When this crosswind increases, the aircraft will as a result drift off the centerline of the runway. To compensate this, you imagine the aircraft speeding up to 'catch' the centerline.

^{Note that I'm not talking about 'forces' - it is helpful to think in velocities only when thinking about crosswinds, and assume the aircraft responds instantly so it only has a forward velocity relative to the wind.}

Now, while this is in theory a way to deal with crosswinds, it's far from ideal. Much better is to simply change your crabbing angle, so that the sideways velocity component (w.r.t. the runway centerline) matches the crosswind. This is much quicker, although it does mean banking is required. You will see that, when the changes in crosswind become too sudden on short final, a go around will be necessary to avoid excessive banking near the ground. Airspeed is kept constant with auto-thrust, not 'crabbing speed'.

From a automation perspective, your suggested way of dealing with crosswinds is entirely possible - an aircraft is capable to detect its lateral and angular deviation from the centerline, and could calculate thrust accordingly. However, physically, a jet engine needs time to spool up to produce the thrust required, and spool down before less thrust can be produced (there is a lot of inertia, and the combustion chamber does not have very relaxed margins as to suddenly injecting extra or removing all fuel).

Furthermore, the airspeed will fluctuate, requiring different angle of attack continuously, and possibly excess velocity on touchdown. Note that when the initial crabbing angle is very small (say, a 1kt crosswind), you would require ludicrous amounts of speed to account for a small increase (the extra speed required varies inversely proportional with the crabbing angle). Conversely, when the initial angle is quite large, you would need to stop in mid-air when the crosswind dies down. All in all, a simple bank to change the crabbing angle is a much more effective way of dealing with a crosswind.

From your question, it seems that you have the following situation:

An aircraft is having a constant angle w.r.t. the runway to compensate for a crosswind. When this crosswind increases, the aircraft will as a result drift off the centerline of the runway. To compensate this, you imagine the aircraft speeding up to 'catch' the centerline.

^{Note that I'm not talking about 'forces' - it is helpful to think in velocities only when thinking about crosswinds, and assume the aircraft responds instantly so it only has a forward velocity relative to the wind.}

Now, while this is in theory a way to deal with crosswinds, it's far from ideal. Much better is to simply change your crabbing angle, so that the sideways velocity component (w.r.t. the runway centerline) matches the crosswind. This is much quicker, although it does mean banking is required. You will see that, when the changes in crosswind become too sudden on short final, a go around will be necessary to avoid excessive banking near the ground. Airspeed is kept constant with auto-thrust, not 'crabbing speed'.

From a automation perspective, your suggested way of dealing with crosswinds is entirely possible - an aircraft is capable to detect its lateral and angular deviation from the centerline, and could calculate thrust accordingly. However, physically, a jet engine needs time to spool up to produce the thrust required, and spool down before less thrust can be produced (there is a lot of inertia, and the combustion chamber does not have very relaxed margins as to suddenly injecting extra or removing all fuel).

Furthermore, the airspeed will fluctuate, requiring different angle of attack continuously, and possibly excess velocity on touchdown. Note that when the initial crabbing angle is very small (say, a 1kt crosswind), you would require ludicrous amounts of speed to account for a small increase (the extra speed required varies inversely proportional with the crabbing angle). Conversely, when the initial angle is quite large, you would need to stop in mid-air when the crosswind dies down. All in all, a simple bank to change the crabbing angle is a much more effective way of dealing with a crosswind.