No, the ants all pay into the system, leveraging the economy of scale, so that everyone has equal access to health care, rather than privileged access for those who can afford it.
You're describing a mutual society, which is a voluntary thing, and very different in character and consequences to compulsory taxation and a welfare state.
Or, you know, the ants work together to achieve something greater than they could ever achieve alone. Ants are quite famous for that.
What part of 'working together' involves people who don't want to?