The one pitfall I was told about was something called a "free-rider problem", which in this specific context doesn't have its normal economic meaning and refers to people taking up public-transit resources while not actually trying to get from Point A to Point B.
Just for example, if your transit is clean, safe, supervised, a moderate temperature, and has long journeys, what fraction of its users will be using it to get somewhere vs. using it because it is a safe place to be?
In the Bay Area, there is "Hotel 22", the Santa Clara Valley Transportation Authority #22 bus from Eastridge Transit Center to Palo Alto Transit Center, about a two-hour ride running 24 hours a day (see e.g. https://www.telegraph.co.uk/news/worldnews/northamerica/usa/... or https://www.mercurynews.com/2013/10/31/homeless-turn-overnig... - a safe warm place to sleep for $6).
In Pynchon's "V" there is Benny Profane "yo-yoing" on the 42nd Street Shuttle from Grand Central to Times Square, but his contemporaries were certainly finding shelter there: https://harpers.org/archive/1956/03/subways-are-for-sleeping...
These aren't necessarily bad side effects but understanding how folks will use the system when it's free is an important part of making the policy decision to make it free.