Consider that it's possible that the person's partner may have exposed them to their then-unknown extra partners, creating one of the conditions for the divorce.
There are other STDs that you'd still be at risk of getting/giving in the case of infidelity, so getting this one vaccine doesn't actually make things all good. I imagine for some people, the thought of possibly bringing home a disease would actually be a sufficient deterrent to prevent infidelity. Not just because they wouldn't want to infect their partner, but because they know it could lead to them getting caught.
I'll elaborate: if you are worried about being unfaithful, or your spouse being unfaithful, then protecting yourself against one STD might seem like a good idea. And if the risk of unfaithfulness is very high, then it is better to mitigate one STD rather than none.
But the fact remains that you are still at risk of many other STDs, so you can still bring home (or have brought home) plenty of other diseases.
The last point, which I knew some people here would dislike, is that the possibility of HPV transmission could, on the margin, discourage some people from being unfaithful. This is because it would be a telltale sign of infidelity, and would cause the spouse to investigate.
Granted, this is only the case where the spouse knew he/she did not have HPV before (mostly people who remained celibate before marriage). If you had many partners before marriage, this advice probably doesn't resonate, but for people who did it makes perfect sense. It acknowledges the risk of infidelity and creates additional accountability by not shielding one's self from a likely telltale sign.
Think about your future health while your mind is clear. After the trauma of divorce is not the time.
Also, I think these questions are in bad faith.
It is actually hard to get people to change any behavior. The public health benefits should be a primary concern. Avoid vaccination if there is a downside to you personally, but that isn’t what I’m hearing from your comments.