So this is specific to your employer? Because I know a lot of people who were under the impression their insurance was “part of the package” and that they “had to get it through work.” Both patently false. I’m sure SOME places have it rigged up like that, I just haven’t encountered it. Have you clarified this with HR?
Yes. Employers allow people to opt out (for example, their spouse has a better plan from their employer.) Some employers will actually pay a small amount of the money that is paid for insurance to you if you opt out (i.e. to encourage people to go with the spouse's plan and save the company money.)
I have never heard of any company paying employees the FULL amount that would be paid for insurance if the employee opts out. Even if they did, the money would be taxed at your marginal rate, leaving MUCH less money to buy insurance in the market.
Is it technically feasible to get insurance apart from your employer when you have a salary/benefits job - Yes. Is it practical - Not really.