What if we had a way of making buildings of a given size, or, say, value, contribute cash to the local and state governments, that the governments could then distribute as needed to transit, emergency services, infrastructure, schools, etc? We could even make it an annual fee so that they have to contribute to ongoing costs, and maybe periodically we could reassess the value of the property.

Sounds like it would be wildly unpopular and politicians would mess with your figures to get votes, even when that would ruin the budget. Sometimes specifically to ruin the budget because what they really want is to reduce/remove those services.

GP described the current property tax system, which seems to work pretty well in non-blighted towns and cities.

Impact fees on new developments are already a thing to pay for other infrastructure improvements like sewer, utilities, roads, and parks. No reason it couldn't be extended to transit as well.

Property owners already pay property taxes to fund infrastructure. Larger developments pay more in taxes (and the residents who live there pay income taxes etc.)

"Impact fees" are just a way to discourage new development.

That's a tax on new construction which will reduce it. Tax all homeowners equally.

Isn’t that somewhat counterproductive if you are trying to attract developers to build in your cities urban core? They might decide to just build in the suburbs or another city that pencils out better.