The OP argument 'everyone uses it' is also not super rational argument either on it's face - we all 'use food' and 'water' but we pay for those - the former in market terms, and the later is socialized on some level but still paid for by individuals on a usage basis.
1) You'd be happy to have people in villages and in the countryside pay for your transportation, who wouldn't? It's not fair or ideal, to have some people's tax money pushed heavily into systems that don't benefit them.
2) When things are 'free' we tend to use them in a way that does not reflect their true cost. Imagine if toilet paper were 'free' for everyone. We'd probably use a lot more of it, unnecessarily so.
The issue with metros is the intense capital costs and de facto monopoly status.
If there were 20 metros too choose from we wouldn't even think of socializing them, you'd just have to 'pay for it' literally like everything else.
The 'Strategic Advantage' in the metro is that it's actually a very efficient way to move people, but those efficiencies may not be realizable without subsidy.
So instead of 'free' - a reasonable solution might be to subsidize expansion while requiring regular Ops to be paid for out of revenue. Some investment in urban facilities is warranted vis-a-vis the countryside due to the big upside i.e. a large bit of social/industrial gain can be had by government investment that could not be had otherwise.