it's not a subsidy if it's a user-pays system.

A subsidy is only a subsidy if users don't necessarily pay the full cost, and the rest is borne by some other group of people who _don't_ use the service.

One issue is that people often benefit from infrastructure without explicitly using it.

Example, road network isn't paid by car owners. But non-drivers clearly benefit from the road network, is the road network subsidized?

Other example, people who rarely take the train still benefit from rail infrastructure (freight, reduced congestion etc). Is the rail network subsidized?

Oh to clarify on that point, the majority of roadwork is paid for by property taxes in I believe everywhere in the USA. Certainly in Texas.