I certainly don't think the US Healthcare model is special
But I don't think any model will be particularly advantaged at handling an overloaded system because of hysteria. It sounds like Canada has a good setup according to what you said, but I'd wager that's more because of being organized and sensible (and having such a small amount of people testing positive) rather than their actual system.
As long as everyone's crazy and thinks this is the apocalypse systems will be overloaded. I think public relations will do more to combat this than any medical interventions
Social healthcare systems are better equipped because they can funnel the populace as a group into a single process, but of course if the process isn't right or properly resourced then it also falls down. The UK has that problem currently as it wants people who think they might have symptoms to first call the NHS 111 hotline, which means of course every queynte with a weird pimple is calling up to see if it means they have coronavirus and as a result people are having to sit on hold for hours on end to get answered because British people are freaking idiots who love a good panic.
In Canada we seem to have a handle on it, we're doing a similar thing with pointing people initially to their provincial telehealth service - I imagine they're busy but I haven't heard of them being overwhelmed. If telehealth determines that you sound like you are a risk of positive (symptoms, high risk travel etc) then they're directing you to your local testing centre with a referral number - without a referral you don't get tested.
In the US I suspect the risk is that walk in centres and ERs will take the brunt of the uninsured, or worse, people who are actually infected but have no coverage will just soldier on and keep spreading it. We shall see.