Density means access to more things/people with the same or less resources (walking is significantly cheaper than driving). That's what freedom is.
The average annual cost of owning and operating a private vehicle is about $8,500[1].
The median personal income in the US is about $31,000[2].
Clearly, for a large part of the population, a good proportion of their working hours are spent paying for transportation. They are "paying huge sums of time".
If you are only bringing in the median income, not being obliged to run a car is a massive advantage. Yes, of course you will miss out on some things such as going camping on the weekend but if this were really important to you then hiring a car specifically for this purpose would be a good option.
[1] https://www.rita.dot.gov/bts/sites/rita.dot.gov.bts/files/pu...
[2] https://en.wikipedia.org/wiki/Personal_income_in_the_United_...
If you have access to 10 identical Chuck E. Cheese's restaurants with a 10 minutes drive, you have less access than if you have access to 10 very different restaurants with a 10 min walk as it's typically the case in a dense city center.
I agree that the relevant metric is time. In a dense environment, you typically have access to more and more diverse things than in a less dense, car dependent suburban environment, in the same amount of time.