Would it be possible to allow Audacity to drop into record while playing? If so, are there reasons for not doing so? This would often be a real benefit - well, at least to me 
If you mean Crash Record, no Audacity won’t do that. You can use the Overdubbing tools and Play and Record at the same time. Play the old track at the same time you’re recording a new one underneath it. This is the technique you would use to sing three part harmony to yourself.
http://manual.audacityteam.org/o/man/tutorial_recording_multi_track_overdubs.html
Koz