I'm a little late to the game, but must voice a strong concern with the proposal.
"Transit" in American English almost invariably refers to public transportation. It's in the names of major agencies such as New Jersey Transit and the San Diego Metropolitan Transit System, and for that matter Google Transit. Merriam-Webster gives the last part of the primary definition of "transit" as
local transportation especially of people by public conveyance;
While questions heretofore may have been about air travel, as this site gains momentum I can easily see someone asking "Can I get from LAX to Olvera Street by transit?" or "What are my transit options on Christmas in Atlanta?" and tagging the question in the same way.
Anecdotally, I would say the terminology "transit passenger" is significantly less common than "connecting passenger" outside of those in the travel industry, not surprising because the overwhelming majority of flights are domestic, unlike most of the world, and I think most concerns about being in transit relate to customs and immigration questions.
So, I would certainly not consider transit to be a synonym of connection, and would see if it can be "salted" to force someone to choose between connection and public transport.