Yup. Premiums change depending on the deductible you choose[1] and your age.

[1]: If you have the CHF2500/year deductible, premiums are cheaper but you have to pay that amount out of picket before the insurance company reimburses your expenses

Obama tried this and America lost its mind.

Isn't this how socialized healthcare works in every country? Whether they realize it or not the principle is generally the same, an amount (usually bundled under "social contributions") goes from people's gross salary to pay for the health insurance.

In other EU countries it's the same or even worse: you just pay it as a part of gross and gross-gross taxes.