Using monopsonic position to keep costs as low as possible is a primary advantage of single payer healthcare. And raising healthcare payroll taxes is politically unpopular like raising any other taxes. No need to spread conspiracy theories about preparation for privatizations.
I feel that the bigger problem is that the demographic bomb has finally hit more developed countries beyond Canada. Unlike either the US or Canada, Europe just isn’t very used to immigration yet. The EU is nearly as good at assimilation compare to the US because they’re still relatively new to the game, which exacerbates the problems associated with immigration. Of course countries in Asia, like Japan and South Korea, are even worse than the EU when it comes to assimilation