It did change the political situation, though. Since we don't know why the UFP agreed to giving up a piece of technology, we can but speculate that they got something in return from the Romulans. And since we never hear of the Feds getting technology from the Romulans, or territory, or the UFP believing in monetary bribes, we can but speculate the Romulans gave them political concessions. Such as "We don't launch the war to end all wars by using our cloaked ships if you agree not to cloak". These concessions could well grow outdated in the course of the Dominion War.
Coupled to this was that the Federation had no known means of detecting cloaked ships.
They did have various means - but they only came up with a halfway effective one in "Redemption", by setting up tripwires of tachyon radiation. And by the time of "Face of the Enemy", they had adopted the tachyon network as a means of guarding strategically important stretches of their border, so effectively that the Romulan cloakships could now only penetrate if getting help from espionage operations. That alone might have rendered Algeron outdated already.
but the Dominion used anti-polaron beams to track them.
Those only worked at point-blank ranges, if then. However, the Dominion also had some better sensor technology that could work across whole sectors: that's what Dax was sent to destroy, off screen, in "Behind the Lines". And that would have outdated Alpha Quadrant cloaking technology, and treaties based on it, overnight. Assuming that Alpha Quadrant powers got hold of the sensor tech and managed to reverse-engineer it (probably not too easy), or at least managed to fool their enemies into thinking that they had done so (probably a bit easier).
During the War, there was little to stop the Federation from capturing a Dominion ship, and analysing how the anti-polaron technology works.
But as said, that tech was almost useless. You could have two ships scanning you from less than a kilometer away and failing to see you, as in "The Search". You'd have far more success just firing around blindly with your phasers!
Also, the Romulans may not be able to make a counter-measure immediately. it could take them years, or even decades.
Against the sensor tech of "Behind the Lines", it might take centuries. The Dominion did have pretty advanced technology, even if they were duly impressed by Federation tech and engineering in return.
So if the Romulans only value peace with the Federation since they have cloaks and the Federation does not, then Dominion technology undermines this advantage, no?
I don't think so - because as said, the Feds do have pretty good sensor technology already in "Face of the Enemy". The war wouldn't change that.
Keeping the enemy from (officially) having cloaks is always a pretty good advantage, regardless of the state of sensory art, because then the enemy is incapable of doing cloaked nastiness even in those areas of space where your sensor nets are incomplete (which is probably always more than 99% of space, since space
is big). But one needs really strong leverage to keep the enemy from having cloaks (even officially, let alone clandestinely), and that leverage might have been lost in the war. Or perhaps decades before the war, but nobody wanted to rattle status quo until they had to.
Timo Saloniemi