Cherry-picking a few nuggets from the excellent discussion.
Tankers: I think the real purpose of these ships in the TU is to provide the option for rapid transit when you really, really need to minimize your travel time. Harking back to the FFW PBEM, by using tankers the Zhodani were able to "blitz" a few fleets fairly deep into Imperial space. This let their unstreamlined BatRons keep up with the skimmers. The other fleets lagged far to the rear. I don't think there would be a lot of tankers about, and drawing on the FFW boardgame (perilous, I know) there aren't very many in the OTU. But each navy big enough to have a need to move fast - or which thinks it does - will have a few TankerRons around to enable those strike forces.
Hospital ships: Good points about low berths, Bill. I will point out that we still use a few hospital ships today (Google about for the hospital ship Comfort, home-ported in Baltimore[/i] for those situations where we don't yet have the hospital or evac-to-Frankfort capability in place, such as the early stages of the current conflict in Iraq.
I see a possible role for hospital ships in treating those middle-ground cases during long-running planetary operations in order to return these troops to combat status, at least in the early stages before dirtside hospitals are in place, or perhaps on the tail end when they're being evacuated (though at that point, you're probably just tossing them into the low berths as you prepare to scoot). Consider the Zhodani sieges of Efate or Jewell. Sure, you could just freeze these cases until you landed your Army medical teams, but perhaps you could return the soldiers to their units more quickly by treating them. Dunno.
Hospital ships also support disaster relief missions (as the Comfort has done on occaision). ISTR some mention of the IN helping out after a disaster in a JTAS item somewhere.
Still, I think you're probably correct that we're thinking of MASH, or perhaps of the extensive use of hospital ships in WWII.
Consumables: Well, you certainly can't resupply a squadron of Tigresses and their escorts at a lot of worlds in the Marches, for example, so just like the tankers, there is probably a small number of dromedaries to support those times you really need to move fast.
I think the real need for logistics vessels is to support planetside operations. Ground troops in combat go through simply amazing amounts of specialized supplies, and chances are you're shipping that stuff in, at least in the areas the Imperium expects to fight. Sure, you can potentially find food locally, but how about battledress spares? Tankers might provide "secure" havens for refuelling Army areospace fighters in orbit. Might be a small need for orbital repair facilities as well, though I think a case could be made for the Army to actually have a few "jeep carrier" ships to handle these needs. (Boy, there's a curve ball to throw! "Yes, this ship's crew is UA. Got a problem with that?")
Cheers,
John