Have you looked at Nordic countries? At least Finland's state welfare system says that if you already live in EU country, you can apply to get treated in here for the same price as what we (Finns) pay. You can still do walk-ins without an application, but you might be billed "the true cost" of treatments, which for an x-ray (which you mentioned down below) seems to be around 200 euros. Although, if you already know you need one, then you can just use private sector which bills you around 75 euros for one (x-ray). The legislation clearly states that you as a patient would be handled equally. The public sector can't either turn you away in any situation if they already provide the needed care.
The system here is a safe haven in other means as well. As a citizen, you are qualified for equal treatment and costs to those in your hometown in other EU countries as well. You can be abroad for up to a year and any medical emergency within the EU would be covered by the state. It's almost backward but I feel like my peers don't want to travel as much when they are young, partly because they know the medical systems in other parts of the world can screw them up.
The system here is a safe haven in other means as well. As a citizen, you are qualified for equal treatment and costs to those in your hometown in other EU countries as well. You can be abroad for up to a year and any medical emergency within the EU would be covered by the state. It's almost backward but I feel like my peers don't want to travel as much when they are young, partly because they know the medical systems in other parts of the world can screw them up.