Companies need to control healthcare costs which are quite high in the US. Things like screening etc. theoretically should help by catching diseases earlier starting prevention earlier.
In Europe healthcare costs are just another tax, which rate is set by goverment and your employer is just responsible for substracting that from your salary and transfering to government's bank account, but has no say about how much you should pay.The plus side is that your employer simply does not give a damn about your lifestyle choices.
In the US you can't get lower tier quality for a lower price. Literally every other industry has this.
In Europe HC costs are going up as well so your argument is invalid.
Employers still want you to be healthy because they don't want you taking days off work sick. In-service death benefits from heart attacks or whatever could be hundreds of thousands of euros and they still pay them even if you have a national health service. It's probably cheaper to pay for a gym than sick days and in-death benefits.
1. Not all employers will care, and that fact alone gives you some choice.
2. Even employers that do care can only encourage you to live healty lifestyle but cannot punish you for not following their recomendations (financialy or otherwise)
If you want to speak intelligently on the subject, identify a country and compare and contrast with the US.