This seemed like a bad idea to me before the stage grew significantly for v1.1, and now is seems to be a really bad idea. Horizontal is where the stage wants to be... I'd prefer to get it there in a controlled manner.
But, I do think Jim's on top approach could work well for a Retriever that approached the landed stage, extended and set outriggers, engaged the thrust structure on close and two adjacent sides and then latched the top with a clamshell on a extendable boom. Once secured and lifted to unweight the landing legs, the vehicle could be safed and the legs be retracted/removed (the vertical, full weight would rest on the thrust structure which is obviously strong enough). With legs out of the way, the stage could be lowered onto a transport bed with no interference from the Retriever which is 'behind' the stage relative to the transport vehicle.
Such a "retriever" could also be used to put horizontal stages onto the TEL, if properly engineered. As a note, the thread I referenced a few posts back where we were talking about GSE had a fair few posts thinking about what it might be like to never take the stage horizontal at all. IIRC, MeekGee had put a fair bit of thought into that.
It has to do with the facility layout. If you have an "airport-like" environment - everything flat and large, and you basically want to move the landed stage 500 m from landing to hangar to pad, then I don't see an issue with transport. Quite on the contrary - a lot less operations if you keep it vertical.
If on the other hand you need to take it along sloping windy roads like in VB, then forgettaboutit.
Also, even for FH, if you're talking one operation per day (so one flight every 3-4 days) then really, take your time. If you want to fly an FH daily, so are talking about hours worth of turn around, then it gets tight.
As for storage - a queued stage is a non-flying stage. In a commercial airliner fleet, airplanes are either in service or in MRO - but not idle.
Stage maintenance/refurbishment is best achieved when vertical and you can access all parts of the rocket simultaneously.
In the preamble to the whole vertical processing thread, I stated that the motivation for it was that you can access all parts of the rocket at the same time (and avoid two rotations). This assumed that during stage turn-around, the bottleneck is per-engine work, since there are 9 of them. If the stage is truly gas-n-go, then this bottleneck is resolved, and the same consideration then moves to stage MRO, as described above.
Elon's comment was that the "ultimate
goal" is gas-and-go. On the one hand, it validates that he is planning it for F9 (if I remember the context of the comment correctly). On the other, by saying "ultimate", it's also a hint that there's at least one more iteration of F9 before they get there, which was expected.