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.
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.
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.
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.