More importantly, not every protagonist succeeds.
Oh absolutely.
Perhaps the most defining instance of this is me a media where the protagonists absolutely fail in their overall goal, only succeeding in ending the threat long after they needed to. Hellsing Ultimate to my eye is the proactive approach to a antagonist, they are bested, defeated, killed but it occurs only in the antagonist's own time frame, when it came the time for him to die according to his own plan.
The antagonist is victorious in each of his aims, his promise is fulfilled, his own personal ambition is fulfilled and he gave the world a spectacle it will never forget. London is obliterated, its population of five million nearly all dead, the British capital the target of his operation was defeated, humbled just as his men had wished (in accordance with the 1,000 wishes) they had reignited the war of their youth for a single evening. His personal foil was humbled, no longer the container of the fearsome powers that allowed him to skirt the line between the living and the dead.
The protagonist ultimately labels this 'success' as not a war as the antagonist claimed it was but as a mere terrorist act, even so that title rings hollow when you level it at the sheer scope of the carnage that even three decades has yet to ease.
Video relevant to the topic.
Of course you could argue that ultimately all of the antagonist's success will eventually be erased by time but that is something unavoidable, eventually people rebuild, new settlers move where the fallen lay years prior, new members join organizations that were depleted during the attack, the British government continues to operate, the Zepplin Affair as the attack would be known in its aftermath is labeled as a simple terrorist incident, abet the most successful one in terms of taking life in history. Ultimately however in terms of narrative portrayal? The bad guy wins here, he had got the mass death he sought, he gave his men their war, it took decades for Dracula to revive and his new form is absent from its other incarnation's fearsome power, in death, in what would be construed as defeat in a conventional story the Major has changed what was immutable, has followed through with his own objectives and in hindsight despite the revival of the Protagonist, the rebuilding of what was destroyed it does not change the fact that thirty years prior it wasn't the protagonist smiling, it was a pudgy war crazed Major.