The Federation is surrounded by enemies hell-bent on using their military might to subjugate everybody, or destroy those they can't subjugate. The Federation perseveres nevertheless. It thus appears that Starfleet is an utterly dominant military force to begin with, and would not need to cower in front of any adversary.
But that in itself makes the Treaty of Algeron reasonable enough. Take the already nigh-invincible Starfleet and add cloaking devices, and the universe will stand no chance against the ruthless conquistadors of the Federation. Better to perish in hopelessly suicidal wars of Armageddon than to let that happen, then!
So the UFP can choose between having to fight a thousand species in the ultimate struggle of paranoia, and giving up cloaks as a goodwill gesture that really costs them nothing. It's not as if cloaking would really be needed to defeat the wussy Cardassians or Talarians or Tzenkethi, and if refraining from using it saves the UFP from the embarrassment of having to defeat a joint Cardassian-Talarian-Tzenkethi force, let alone from having to ward off genocidal attacks from a desperate Romulan Star Empire...
I guess it could be that Star Fleet felt as if the military advantage of the cloak could be defeated or mitigated with the Neutral Zone sensor net, and patrols. It also seems that it was more of a cold war situation with the Romulans, as long as the Balance of Power was maintained, nothing was going to happen along the zone. Stealing the newer cloaking device was just to maintain that balance.