This would have implied more tense relations with the Empire and most likely far less cooperation before and during the Dominion War, i.e. the Defiant would not have been equipped with a Romulan cloaking device.
If there was no treaty, the Federation could just make their own cloaking device and the romulans were not helpful in the lead up to the Dominion war, until the Federation used some rather dirty tactics to trick the Romulans into the war. The Romulans were not helpful, period.
I don't see any benefits as I doubt that the Romulans stop to be Romulans just because of a bit of Federation sabre-rattling. Sure, they might not do something like the Trojan Horse mission again but they will surely reallocate their forces and attention upon the Federation border. Spock's underground movement will have a much harder time to flourish in such a tense 'drums of war' climate.
After all you don't talk about a minor treaty, the Treaty of Algeron is THE peace treaty between the UFP and the Empire.
And in the several years between Unification and when Romulus blew up, how successful was this underground group at changing anything, it seems like they failed at their objective. By Star trek: Nemesis, the Romulan military seemed more willing to start a war, not less.
Its a peace the Empire undermined all the time, not a true peace. Why should the Federation believe that the Romulans wouldn't pull stunt like the one they tried to pull in "Unification". Wouldn't people in the federation have become far more distrustful of the Romulans and see the peace treaty as the sham that it truly.
Another problem is the lack of evidence of the Trojan Horse mission, the Rommies blew the ships up. Sure, both sides know very well what really happened but appearances matter, the Romulans can pretend to not know what the Feds are talking about and portray the recent developments as unilateral peace-endangering behaviour in front of other major powers like the Klingons who don't know about the Trojan Horse mission unless they have very fine intelligence services.
There was enough circumstantial evidence that led the Enterprise to discover this plot in the first place, Spock sending that message and the romulans blowing up those ships are pretty clear signs of guilt. Appearances are strong to have the diplomatic advantage after that, but the Federation did not exercise.
It's a tricky game and one has to play it as cunningly as the Romulans. Brute force, aggressive posturing or blunt threats seem like the wrong way to deal with this silent enemy. In my opinion endangering the peace treaty just to prove a point, better a truthful war than a fake peace, is foolish in my opinion. Of course it is a fake peace, of course you always have to be vigilante with the Romulans. But it is a form of peace nonetheless and it is preferable to war. You can't expect more than a fake peace if you deal with people whose main dogma is unlimited expansion.
And I think its foolish to give up an important strategic advantage for a peace treaty the other side has no real respect for. That's not diplomacy, that's just knuckling under.
Plus if the Federation simply pulled out the treaty, that wouldn't be an act of war, that would just mean that particular treaty is at an end. Its not like the Federation would just start blasting Romulan ships after that, the treaty ended because the Romulans have been acting in bad faith. They can always sign a new treaty and actually honor it and if the Romulans start shooting, the war would be their fault, not the Federation's. All the Federation did was pull out of the treaty because the other side was not acting in good faith. The Romulans seemed to want avoid a direct conflict, preferring to try to draw the Federation into a conflict, it seems unlikely they would go for a direct conflict.
Sometimes you have to stand up to a bully, otherwise the bully thinks he just push you around whenever he wants.