Gate-towns

It empowers the plane in question. Dramatically. When the the Abyss swallows up a gate-town, it empowers the entire tanar'ri race relative to the baatezu.

In some cases, most of the inhabitants desire it (like the Hardheads of Fortitude saw it as a sign that their philosophy was working, everything progressing toward greater accord).

Certain Tanar'ri have something to gain with a Gate-town shift.

It's likely that Red Shroud for example, might have more territory in Broken Reach, and therefore more power if Plague-Mort shifted over.

Nothing measurable at the level of an individual tanar'ri, but the race as a whole would be empowered. The souls of everyone who lived in the gate-town would be claimed by the Abyss, of course, and the Abyss would gain a prized piece of psychic real estate. Of course, all the planes are infinite, but not all parts of every plane are equally potent. A gate-town offers a new influx of energy and suffering that the plane can devour and make use of.

I expect you'd quickly see the difference on the Blood War fields every time a version of Plague-Mort is swallowed up. And the same is true every time Baator swallows up a version of Ribcage or Darkspine.

Exactly how much difference is up to you. I'm sure a single town, or even a dozen, isn't enough to win the thing, but they add up. With the two sides balanced so closely, it wouldn't take many. I think gate-towns are important, and saving them (or at least balancing how they slide) can be crucial.

How is that supposed to mean when both races are said field bazillions of 'soldiers'? A million or two (or maybe just a few thousand) would make a difference, in a single battle or campaign, but in the war as a whole?
I also think it makes a difference - in the long run. Very long. Short term gain might be relevant for who ever gets their hands on the respective town.
But we should consider a motiv that is (as I think) unbearably underrated in Planescape (and D&D in general): Prestige. The hunger for recognition drives people insane and blind, it most certainly moves the planes as well. I'd also think about tradition, social desirability and such, although we're talking about chaotic folks.

Ironically, thats the same a devil might feel when he's torturing a precious captive. Names and reality have a strange relationship, though the Gate Towns' names seem to fit in one way or the other.

I thought the same about the gates themselfs. So the Towns are something like the symbolization of the symbolization of a symbol. Or so. Anyway, I think such an emphasis on the Gate Towns as sources of power would be a threat to the inner consistense or balance of the setting, degrating other factors like politics, petitioners, military organization (in the Blood War) and so forth.

That may be correct from the macroperspective. But for the individual fiend? Also, I see power and prestige as two distinct forces, although they often come together. And again, what power and prestige mean to a singe person (fiend) is something different from what they might mean to the race or the great shemes of the multiverse.

Yup. That said, I never wanted to suggest that it would be pointless to make a Gate Town shift.