Not surprising that there would still be a lot of use of cars and public transit. If everybody transported everywhere, the 'bandwidth' may have become crowded and prone to malfunctions. Besides there would have to be transporter stations everywhere which would tend to ruin the landscape.
I don't actually believe that humanity would ever change enough for "public sex" - not sure where I ever heard of Roddenberry advocating that?
Possibly derived from Gene's concept of "new humans", which IIRC had a rudimentary collective consciousness (or at least could generate one), walked around naked all the time, hated Starfleet and any kind of authority structure, the type of thing that you would not be at all surprised Gene could come up with (especially if you read the novelization of TMP