OK, but that kinda takes all the fun out...
I'm really curious about this, and I'd probably press a vet on why or why not.
My
SWAG is that the ointment may collect more dirt than it keeps out and/or not wanting it to be ingested, but... (
?
Dunno). I may ask a vet friend about it if I happen to think of it, but for pandemic reasons, I have no idea when that might be.
WOW! That right there is enough to make me ignore everything he said! (
KIDDING! 
)

+1

The only difference I find between neo- & poly- sporins is that:
For cleaning, I would think peroxide should be safe (I would
NOT use alcohol). There should be info on this in the archives.
FWIW, the cut didn't look all that bad to me, but I know the eyes of a concerned "parent" can make a paper cut look like the Grand Canyon. Here's a similar thread in the Health forum right now:
https://www.chameleonforums.com/threads/strange-cut-on-his-foot.177272/
Looks like a similar-sized cut as well.
The difference in whether to use an ointment or not is (IMO) location of the cut. In this thread, it's on the bottom of the foot where it's likely to get dirt in it, whereas the other cut is on the elbow, where it's less likely to get dirt in it.