I mean, you do have to worry about that. It's just that you're happy with what it covers, so you don't worry about it. Despite all the well known awful problems we have, most people in the US actual feel the same about our plans as you do about yours. I don't have to worry about what my insurance covers because it is a good plan, and if it becomes worse, I can look for a better one. This is true for most people in the US - mostly those of us fortunate enough to have good employer sponsored plans - it just isn't true for enough of us in a lot of peoples' opinion (which I share).

One thing I'm way more afraid of with a single payer system (but not necessarily all universal coverage systems) is that if the coverage became worse, I would have no recourse; it would be a monopoly, I wouldn't be able to look for a better competitor. Even worse, it would be a monopoly run by a political bureaucracy, so coverage decisions could become political. For example, coverage for birth control is a very political topic here. I'm certain that the first incarnation of a single payer system would cover that, because it would be set up by the politicians who favor it, but once the system is enshrined, whoever is in power would be able to change it however they think best. Coverage policy could easily become a political football.