I don't have free parking, I pay $150/month for it.
But I'm also a wealthy techie who happens to live within spitting distance of a booming downtown. 90% of the people living in my metro area (Seattle) do not pay $150/month for parking (And I'd wager that 99.9% do not pay $400/month for parking).
... And most of those people have commutes of >4 miles. The problem with taxis is that you pay by the mile. You'd be an idiot to drive yourself to work, if you live 2 miles from work, and have to pay through the nose for parking. You'd be an idiot not to drive yourself to work, if you live 15 miles from work, your bus system sucks, and your parking is cheap or free. [1]
Doing 15 miles/day in a taxi costs nearly 3x that of doing 5 miles/day in a taxi. Doing 15 miles/day in a car is pocket change, compared to doing 5 miles/day in a car (Or 0 miles/day). Most of your costs with a car are fixed. Most of your costs with a taxi are distance-based.
[1] And if we're going to get into a discussion about how the world should value the cost of parking spaces, I will happily point out that what we should have is good bus services, not private chauffeurs.