I believe that perseverance of the saints (POTS) is a true doctrine, and there are plenty of Bible verses that teach or suggest that believers will be kept to the end and will not aposatatize. However, POTS is merely a benefit believers receive in Christ. If Christ really accomplished everything necessary for salvation, then POTS cannot be a cause or necessary effect of salvation. In other words, because the Divine righteousness accomplished by Christ on the cross is all-sufficient for justification and salvation, it precludes the necessity of POTS. Christ's life, death, and resurrection serve as the substitute for the believer's life in the world. This means that, hypothetically speaking, the benefit of POTS could be withheld from the believer for a purpose only known to the inscrutable counsel of God, and yet the believer still be secure as one of God's elect destined for eternal glory. And why should this be surprising? We make exceptions for elect children who die in infancy and others incapacitated, although faith is another benefit in Christ that is given to the elect. If it is okay to make exceptions for faith, why not POTS? Doesn't Christ get all the glory? And what if He wants to show the riches of His glory in such exceptional cases?
It is a grave error to teach that POTS is a grounds of final salvation (e.g., John Piper) or a necessary proof of salvation (e.g., typical Reformed theologian). For John Piper, POTS is an element of salvation. For the typical Reformed theologian, POTS is inherent in salvation. In either case, POTS is required of salvation. This is why I say that there is not much difference between what John Piper teaches and what the typical Reformed theologian teaches. They describe things differently, but arrive at the same conclusions. In the end, they both teach a form of works salvation where the work of Christ on the cross needs to be supplemented or accompanied by the work of man. (Of course, just like the Romans Catholics, they'll say that the work of man is really the work of God in man and that it is all by grace, but this line of reasoning is irrelevant because regardless of whether the work is of man or of God in man, they nullify the sufficiency of the work of Christ on the cross by requiring it to be supplemented or accompanied by works.)
To substantiate my assertion that John Piper and Reformed theologians are basically teaching the same thing, I suggest watching the discussion section of the 2022 ETS Annual Meeting here. Although the discussion wasn't about POTS specifically, some of their discussion points fell within the realm of POTS. John Piper defended his viewpoint that saving faith contains an affectional element against Guy Waters and John V. Fesko who argued that saving faith should be limited to the classical Reformed understanding of knowledge, assent, and trust (Latin, fiducia). Although it was two against one, the moderator Joe Rigney, who seemed to be in charge of asking questions, was clearly on the side of John Piper, so actually the cards were stacked in Piper's favor. Nevertheless, it was a good and revealing discussion. What stood out to me was how masterfully Piper and Rigney handled Waters and Fesko, showing that their beliefs basically amount to the same thing when all is said and done.