It wouldn't matter if the vehicle was made for Starfleet.
So we have a flying vehicle in Starfleet colors, transporting a single top officer in comfort (with a pilot plus at least two personnel who make no effort to depart the vehicle after landing and Kirk's egress), operating out of Starfleet Headquarters - and we want to insist that it is evidence for some sort of public transportation? Makes no sense to me.
Sure, there
might exist a public transport system based on flying vehicles in San Francisco, and perhaps in other cities as well. But Kirk's shuttle is hardly pointing in that direction - and if the system of which that shuttle is part extends outside SF HQ, then apparently the evidence we want is stretches of "rail" elsewhere in the city, since apparently those shuttles require such landing aids for some weird reason. We have several rails in view at SF HQ, and three vehicles, two of them larger than Kirk's and with at least two and possibly four doors; now all we need is more rails somewhere else!
One thing people forget about is security. Only trained personnel may use transporters.
I rather doubt that, actually. Only trained people can drive a tank, or a train. But any fool can drive a car, or travel by train. If civilian transporters exist, they are probably well and truly idiotproofed, and locked to only operate on a specific library of destination coordinates.
A civilian transporter might consist of an industrial-strength installation somewhere safe, plus a thousand home "pads" that are really just circles painted on the floor plus a call button on the wall (all stylishly designed, of course). Or/and there could be large terminals where people emerging from an arriving spacecraft or a public event or the like can all rush into and press their wrist selectors to choose an individual destination (much like Tom Paris did in "Non Sequitur"), and the machinery of the terminal sorts out the calls. For those without the wrist units, there'd be rows of booths... Doubling as suicide booths if need be, of course.
Since such systems would have all the hardware in locations the camera doesn't visit, they would support the observed lifestyle where people generally walk, sometimes ride an elevator, and once in a rare while take a flying vehicle. Those trains in Paris might be for sightseeing only...
Then there is no privacy in the Federation.
That's a well-established fact already: our heroes are always scanning various dwellings for lifesigns and their exact coordinates, without any indication that there'd be issues of consent involved.
Timo Saloniemi