In addition to the accurate answer by Neil_UK, I don't know what type of linear PSU design you have seen, but some of them do employ some smart schemes where the wasted power can be optimized by methods that are easy to implement, but would complicate your proposed scheme of estimating heat generation.
My linear PSU has a multitap mains transformer, and a relay (relays?) to choose the tap that is closest to the desired output voltage, so the pass element has to drop the minimal voltage needed. Of course, the heat dissipated is still (Vtap - Vout)×Iout, but it's not easy to measure Vtap - it has some AC ripple on top of it (I guess it is straight after the bridge rectifier and filter caps), and it will also depend on mains power variation (210-250VAC). My linear PSU, as it is now, is designed so that you don't care how much Vtap is (as long as it is within some limits of course), but with your scheme you'd have to measure, filter it, etc. Thus your proposed scheme doesn't necessarily simplify things.