If it is decided by a city government that we want public transport as a public service, paid for by taxes and other means then removing prices is an option that could make sense in the right situations.
The road system doesn't have a price tag per trip, yet it's costs are managed through policy and governance. No difference here in my opinion.
I think your point about economic signals is very good - I wonder if any locality charges at cost; does NYC do it now? - though 'charging at cost' undermines the goals: universal mobility, reducing climate impact, reducing congestion, and (I think) increasing economic liquidity and competition (e.g., in the labor market, in retail, etc.).
We need another solution: Maybe vouchers for people based on income? That becomes much more complex.
Also, I would gues it impacts ease of use and adoption - imagine being able to just hop on any passing bus, as opposed to finding your payment, going only through the front door, paying, etc.
You should charge roughly what it costs to operate because that's information. People should ask why it costs so much. People should consider alternatives. Trying to remove prices is like fighting climate change by removing thermometers.