Interestingly, in some cases the amount of subsidy required may go
down by eliminating fares and the associated collection and ticketing infrastructure. (That doesn't account for changes in ridership level. On the other hand, it also doesn't account for speeding up pickup times by not worrying about fare collection.)
On balance, it's likely more efficient to pay for public transit via approaches like taxes on businesses served by that transit (who will get increased business).
At this point, I don't think fares serve much of a revenue function; they serve as a filtering function, excluding people who can't afford them, and as a PR function, making transit get more votes.
Also, I have a lot of sympathy for "should we subsidize this or not" arguments, but any such argument also needs to take into account how much we subsidize roads. Gas taxes and registration fees don't fully cover the costs of roads, any more than transit fares fully cover the costs of transit.