And A&D ointment likely works because it is what, about 90% to 95% vaseline/petroleum jelly?

I guess it is possible that with that little bit of lanolin, that it might act a bit different that plain vaseline. I don't think the vitamins are going to make a difference.

Bag Balm is almost identical to A&D Ointment. It is mostly petroleum jelly with lanolin added, and then a touch of antiseptic. But the antiseptic used is not approved for use on humans in some countries. Which is why it is sold in the pet section. Many recommend it, but usually to treat sores, not to prevent them.

Neosporin was mentioned by jcm. That's not a bad idea. Again nearly all vaseline, but with "approved for humans" antibiotics. So as a lubricant, it should work almost identically to vaseline, A&D, Bag Balm, and other vaseline/petroletum products and still have the antibiotic action of Assos & Bag Balm (although it should be better in this regard than Bag Balm). You can buy the generic product in places like Dollar Stores pretty cheap.

What I find interesting is that most people go to great lengths (and have done it myself) to avoid buying plain old store-brand petroleum jelly when that works about as good as anything and is far cheaper.

Another vaseline-based product that works wonderfully for chafing is Preparation-H (the ointment, not the cream). This is again nearly 100% petroleum jelly, but with an additive that shrinks and protects irritated tissue. That is what chafing is!