Baby oil is horrible to use for anything and there are many more options out there.
First, it stains sheets. I used to use baby oil all of the time when I was young and lube wasn't that common place. I put baby oil in the same category as those Wesson parties that used to take place in the 70's and early 80's (if I remember right).
Although I really like being messy and slippery, there are other ways to go. Nuru gel is one. Although it IS oil, it's lighter (although it will still stain the sheets) and I would tend to recommend Neutrogena Body Oil, which is made of sesame oil. I keep this in the shower and use it regularly. But again, rarely will I offer to use oils as a massage option.
Baby oil is also awful in terms of using condoms. The actual liquid causes condoms to lose their integrity and using baby oil as a lube is just a bad idea.
You mentioned being a naive old man. Well, you're probably not that naive
BUT ... I've had clients show up with a small bottle of baby oil and they tend to get upset when I tell them that I won't use it unless we're in the shower. Then, it's alright (but I have to clean the tub afterwards!).
Since I'm an older woman, we can talk about what is old and what is new all night long. And I completely understand why baby oil sounds hot.
But with all of the new massage creams, lotions and combinations of lube with the ability to also be used as a massage lotion, there are just so many different directions to go other than the dreaded baby oil.
Best,
Elisabeth