The cost of everything being higher is principally due to rent (in particular land rents). Food, concerts, clothes, coffee, all of them have a "land upon which this was retailed and sold + land upon which the person behind the counter lives" line item. In high-COL areas, this invisible line item makes up a gigantic portion of any bill you pay anywhere.

I'm not sure what the rest of your comment is about? That's fine if you have that preference. Expressing that preference generates negative externalities on the people who do live in the city, and you should have to internalize those costs to whatever degree possible.

Your rents, by the way, do not just pay for your house and land. Your rent pays principally for location. So the idea that you're not engaging in rent arbitrage because you wouldn't want to pay the same amount to have the same unit in Tribeca is nonsense. The question is: would you pay more to have the same house, land, surroundings, and also have immediate access to city amenities and jobs.

The answer to that is already empirically yes. Because you pay the cost you do for your current house, land, surroundings, then you pay an additional cost (an insufficiently internalized one) to commute into the city. Time, tolls, stress, vehicle ownership, parking, etc. So obviously the exact same set of facts minus the commute, despite being physically impossible, would be a more preferable product.

Or to put it another way: would you pay more than $0 to have a teleportation portal from your home in the suburbs to your work in the city. My suspicion is yes.