It's hard to be sure 100%, but I feel like whatever the outcome, this thought experiment doesn't really yield useful information unless you're hoping for the outcome be "they don't really want healthcare, they're just faking their desire for healthcare because they want to take things away from wealthy people". I'm pretty sure the desire for healthcare isn't just a ruse.

After everyone has healthcare, will there be people who desire a more-flattened society? Possibly. There are a lot of different people in the world with a lot of different ideas. But that's a separate conversation.