Your argument is right in principle, but it hides a proving-too-much fallacy.

By a similar reasoning one could claim that waiters/factory workers should also be independent contractors. If they don't like the pay in one business they can go work in another marketplace.

By this contrived example I mean to say that your analysis applies only to the superficial structure of the concept of employment. Ultimately social structures are not axiomatic field and should be treated accordingly.