Considering that most ASF are in the range of 70 to 90 tons, that's a very large element to provide service and landing areas for, also the support areas must be guarded and protected, taking away resources from tracked and legged elements. ASF's are not as maneuverable as standard aero fight's but more heavily armoured and armed. The ASF's would normally be a Regimental or Corp asset and mainly used for DropShip protection during assent and descent where they are much more vulnerable. (as well as the normal Jump ship protection duties)
There are canon stories where mechs do fight ASF's, but any fast air vehicle requiring precise aiming (as we have in this game) normally requires straight runs, and that's where the mech's and tracks bring there quad AC5's and AC2's for specifically that purpose. In this game if your not paying attention, even LRM's will track the ASF and hit. Have seen many times, once a ASF is identified to be "up and about" the pilots quickly bring out the AAA elements.
Just talking out loud here,