It is somewhat popular, so I doubt they will kill it outright. Rather I would guess they "reform" it: lots of variants, much higher price, beaurocratic hoops... and then when people stop using it, say "see, it wasn't so great after all".

Same playbook in the UK, where people like the NHS but certain parties don't.

Same playbook in the US, where "big government" has to be bad, so anything that does currently work well gets sabotaged.

A lot of times it's even worse than this, because what will happen is well-run public services will be sold off to the private sector. Who then runs away with extreme greed granted from the privilege of an inelastic market. So prices soar and quality plummets.

Then, we can point and say "see? Look at how bad it is! It would only be worse if the government ran it!"

Extra points if you're able to extract public funds to waste on such private endeavors. See: private schools in America (Yes, they get public funds!)