The only thing I've never understood about the HPV vaccination is that for some reason after a certain age as an adult in the United States, no primary care provider appears to recommend you get it in addition to your regular vaccination schedule.

Is the idea that you're married and have a single partner and the risk factor has dropped below a certain percentage of the population where there's little reason to recommend getting it if the likelihood is that you've already acquired HPV in your lifetime thus far?

Every other vaccination appears to be straightforward, besides HPV, and I don't know why. I've also never heard a clear answer from a physician.

Is it just that our vaccination schedules are out of date in the United States? This seems to be the most likely culprit to me.

Here's the CDC's most recent recommendations (from 2019) https://www.cdc.gov/mmwr/volumes/68/wr/mm6832a3.htm

The justification for 27-45 year olds heavily references a meeting. Based on time, author and title, I think either https://stacks.cdc.gov/view/cdc/78082/cdc_78082_DS1.pdf or https://pmc.ncbi.nlm.nih.gov/articles/PMC10395540/ should be a fair summary of the meeting (I hope...).

I don't really have time to read it all, but the basic idea is as you said - the cost-benefit ratio is off. Basically expanding from something like the current case, to vaccinating up to 45 year old will avert an extra 21k cases of cancer (compared to the base case of 1.4 million) - so about an extra 1.5% cases averted, while the direct vaccination costs are estimated to increase from 44 billion to 57 billion (+29%).

The current guidance says "do not recommend" plus "consult your doctor". You should read that as "blanket vaccination as public policy is cost inefficient in that age range" not "you as a 45 year old should not get the vaccine categorically".