If someone tasked me with building a data center, I'd probably start by looking at Google Maps and looking for the nearest big, open field on the outskirts of a city.
The other reason is you have employees there who can go fix things when they break. In the early days of Square we had everything in a single datacenter in Mountain View and our office was in San Francisco. There were times when something broke in a bad enough way that someone had to drive to the datacenter. It was a while before we built the scale and redundancy to put a facility on the east cost, or in places where we didn't often go.
But you're right, per square foot it's often quite expensive.
At a certain scale you still buy space in the city for connectivity, but then you buy IP transit, or even dark fiber, to connect to a cheaper and larger facility. That could be in the same region, or it might be out in some farmland with cheap power and good tax incentives.
We've seen lots of datacenters built in Washington and Oregon because the electricity is famously cheap hydroelectric. Like $0.02 - $0.03 per kWh. Last I looked a few (5-7?) years ago, industrial power in the Bay Area was closer to $0.10 per kWh and in Ashburn VA it was $0.08.
2. Office buildings often have some lower-quality space (e.g. areas with no windows) so you don't have to use super-premium office space.
3. Server racks are extremely dense, so they can make a lot of revenue per square foot compared to a lot of land uses. Good luck running a yoga studio that makes more revenue per square foot.
Of course there are disadvantages to city data centres - limited room to expand, and nobody's going to offer you subsidy for "creating jobs".