No I don't think we should be pushing for this. But the doctor's themselves absolutely should.
They've clearly said the renumeration and stress levels in th NHS system are unacceptable. Hence the strikes. Many have signaled that they would rather work in non NHS style health systems because of the pay and quality of life improvements. Good for them.
As hard as it might be to hear this maybe it's time to rethink how well the NHS system is working. Not for patients (but also that) but for the workers within in. A key tranche of which are so pissed off with it that they want to move to Australia.