Did I say that just one city is producing all my units? Well, I guess I did imply it in the lead-in, but my real point was "What's wrong if every unit has Medic 1, as long as it doesn't cost you XP?"
By the time that WP becomes available, I ought to already be cranking out CR 3 units at the HE using Barracks + GGs + 2 (usually Theocracy); if not, I've probably been going light on the warfare. By running Theocracy, of course, any city with a barracks can give me a shock X-bow, a CG 2 Longbow, or an accuracy or barrage cat/treb, or even an inferior CR 2 mace.
Once the HE can produce CR 3 melee units, I don't want it to stop until I can't build melee anymore -- I want as many CR 3 infantry as I can get. And honestly, I don't need my CR 3 units to start with Combat 1 as well. I'll promote them along that line after their battles.
I just don't see how putting WP in with the HE does much good. You're already getting diminishing returns on XP, and since the HE comes so early, you've probably found a better production site, which may come with a free GG or three (and possibly a military academy as well), as a gift from the former owner. So I set up a second high-end military city with WP, which, once it becomes available, will also get the Red Cross. Since it's going to be producing the "special" units for the most part, it can afford to take the turns off to build the RC.
With this setup, it makes more sense to have the HE city to keep cranking out CR 3 whatever (maces, cannons, artillery, tanks) as the assault force, and the WP city to build the more interesting units (which the RC helps with significantly) and military navy, while any other cities are producing the cannon fodder, the soft defense, and the galleons and transports.
If the HE city seems to be struggling to produce a unit every turn or two, I'll throw the IW in while the only thing it can produce at CR 3 or Barrage 3 is siege. Otherwise IW winds up being mostly for wonders and upgrading my defenses. And if I really just need more CR 3 units, I'll go ahead and make some with WP/RC, and give 'em march.
I think we can both agree that "it depends on the circumstances/land/etc. of the particular game." I find that for most games, HE/WP and IW/RC work best.