This is nothing to do with the doctors' strikes. A plumber's charges are not his 'pay'. He will be charging for offtakes, NI, tax, wear and tear of equipment, transport, maybe premises, an accountant, insurance and goodness knows what else before he or she gets anything for him or herself. Doctors, in common with most other employees, are paid after their employers have factored all of that in.
The 'who is more valuable?' debate is massively complicated, and like pretty much everything is political. IMO (as a believer in a large but liberal state) we, collectively, should pay for all training and education for anyone who can benefit from it, and in the case of those whose careers are (or can be) in the public sector this should be in return for a pro-rata contract with the trainee that they will work for a pre-arranged period of time in the role for which they've been trained at a pre-agreed and index linked rate which is clear to both parties at the time of starting the training.
Those going into private sector careers could have additional taxes until their training is paid for. I would have no differential between expensive and cheaper courses - training would be at a flat rate to the trainee, so an engineer who needs expensive equipment to learn on would be paying back no more than someone whose course is book-based and cheaper to teach. I would make it prohibitively expensive, or even impossible for someone trained on a 'public sector' free course to switch to a private sector role before their payback time has elapsed.
That way, if we need more doctors/teachers/town planners, we can pay for them in the knowledge that they will be there for x years, and nobody need be put off going into any profession, trade or whatever because of the cost of training. That would restrict the field to the most talented, not those most able to absorb prohibitive costs. A sensible government (I know, but this is never going to happen anyway 
) could plan for things like surges in the birthrate, an ageing population, or whatever, and ensure that there are enough relevant people to fill the roles that are needed.
I wouldn't exclude poets, musicians and artists from any of this. They would still get free education in the Arts, and would pay taxes on their work washing dishes and waiting tables which is how most make their living, but would stop us from becoming a nation of barbarians. I see them as worthy too. As are hairdressers and other groups who earn little but work hard and improve our lives in different ways.
Differentials in pay are, IMO, necessary, but there shouldn't be as much of a gap as there is now. We all need one another - yes, we can't do without some things (eg ambulance drivers, doctors, care workers), but life would be pretty inconvenient without sewage workers, plumbers and shop assistants and miserable without TV producers, actors, artists and authors.
