(political opinion disclaimer) IMO, that part's basically just "cost-saving" misdirection/smoke screen (eg it's not "public spending" but we're all spending it). I think that lines up with your question about "why both taxes and having to have private on top".
But in general, "people going untreated" is not much of a concern even if, for example, they don't work and don't private insurance.
Also worth noting, though, that the private insurance premiums in France are nothing like in the US (for example), not least because they don't have to cover anywhere near as much.
(political opinion disclaimer) IMO, that part's basically just "cost-saving" misdirection/smoke screen (eg it's not "public spending" but we're all spending it). I think that lines up with your question about "why both taxes and having to have private on top".
But in general, "people going untreated" is not much of a concern even if, for example, they don't work and don't private insurance.