You have no way of knowing if they will ever cover anything except to pick a good company.
The whole idea of saving money instead of buying insurance sounds good but if you don't have a large nest egg to fall back on you would be screwed if you had a major health event or accident especially if this happened in your first year or two here.
Let me say that you are probably going to get the residence certificate and still find you cannot open an account without an agent or extreme luck. Just FYI.