First of all, many more EU/EEA countries have comprehensive healthcare if not single-payer healthcare, so there is less of a divergence in policy in most places.
Secondly, EU freedom of movement isn't as strong. See Directive 2004/38/EC, such as the points reproduced below which AFAIK some countries already take advantage of:
"Union citizens should have the right of residence in the host Member State for a period not exceeding three months without being subject to any conditions or any formalities other than the requirement to hold a valid identity card or passport, without prejudice to a more favourable treatment applicable to job-seekers as recognised by the case-law of the Court of Justice."
"Persons exercising their right of residence should not, however, become an unreasonable burden on the social assistance system of the host Member State during an initial period of residence. Therefore, the right of residence for Union citizens and their family members for periods in excess of three months should be subject to conditions."
Secondly, EU freedom of movement isn't as strong. See Directive 2004/38/EC, such as the points reproduced below which AFAIK some countries already take advantage of:
"Union citizens should have the right of residence in the host Member State for a period not exceeding three months without being subject to any conditions or any formalities other than the requirement to hold a valid identity card or passport, without prejudice to a more favourable treatment applicable to job-seekers as recognised by the case-law of the Court of Justice."
"Persons exercising their right of residence should not, however, become an unreasonable burden on the social assistance system of the host Member State during an initial period of residence. Therefore, the right of residence for Union citizens and their family members for periods in excess of three months should be subject to conditions."