Too complicated approach to a no-existent problem - heating of speaker coils.
Sure the coils heat up and resistance increase. But that's a linear process, does not introduce any distortions. It's enough to turn the volume up if that's an issue.
Only if you are listening to sinewaves. As music (especially anything that is not heavily compressed pop) has a very wide dynamic range only loud passages will cause appreciable heating, compressing them, while the inevitable slow recovery will attenuate anything directly after the peaks... Upping Driver efficiency goes a long way to reduce the issues.
However, current drive deals with other issues I consider more important. Namely one of the main distortion sources in dynamic speakers driven by a low impedance (Eddy Current distortion). Of course there are other ways to deal with this (all the speakers I currently use have this on the midrange), but they have become a little more common only recently and of course again, reducing current by increasing efficiency again works also quite well.
A happy middle ground are above average sensitivity speakers with additional measures taken to reduce eddy current distortion.