It might be if the solution weren't always "worse education for the richest", to harmonise things.
We fundamentally need competition in every sector. Without competition every business is destined for failure because you remove any incentive to be better.
Competition is the absolute key that unlocks success in every walk of life. Competition in performances based salary. Competition in bad organisations going bust (hello Thomas Cook). Competition in bad schools and hospitals being put out of business by good ones.
This doesn't meant 100% free market forces shafting poor people. It means giving everyone the resource to make their own decisions, rather than telling them they must use crap services "because socialism".
If you need surgery and it costs £5k on the NHS, have a voucher system where you can spend this voucher anywhere. Free market forces will mean poor peacticioners fail and gold ones expand. If your shit school costs the government £10k a year per pupil, give parents a voucher and let the parents choose where to spend it.
If state hospitals and education win all the business and the extra competition merely makes them work harder, fantastic. If every single state institution goes bump as private companies are providing better services at the same cost then great also as the patients and pupils are the sole beneficiaries.
Why competition law exists but doesn't apply to state systems is beyond me. Any critical thinker must look at state systems and think "what's the incentive for them to be better".