I think you'll find my math is fine, and I know how to play the game fairly well. You can skip the derision.
In my current game in 1170 AD I have five such cities. Plus several more that I could potentially convert to such a status if I shifted around tiles and citizens.
Because as most Civ veterans know, it's not the later game that matters, it's the early game. By 1200 AD you will often have the game fairly well in the bag (or at least heading that way). Being able to produce stuff more quickly matters less at that point. Barracks, Stable, Armory and Forge all become available fairly early on, and they should become useful at the times when they arrive in the tech tree. Otherwise, why put them in so early if they're of no use until later?
The key to a successful campaign in the early-mid game is to have the strongest army possible. With such low unit numbers overall in Civ5 compared to Civ4 though, buildings like the Barracks/Armory/Stable/Forge are fairly useless in the key early-mid game interval. At present it's better to produce a larger army of non-promoted units than to waste valuable hammers producing buildings which give minimal benefits to your smaller army. It shouldn't be that way. That is the key point I have been trying to make here.
If you truly don't need the units, you're wasting your time building them given that there are so many other things to build. But I don't see how you could ever not need the units until you win the game. If you're producing units and then deleting them immediately, you're probably doing it wrong (unless you're not going for a Conquest victory).