Applying Rust Killer to under carriage /frame any reason not to ?

The Ospho site doesn't actually "say" to neutralize it. It says let it dry and wipe down with mineral spirits before painting.

Ospho

If you go to SouthernPolyurethanes site it gives lots of tech info on all their products, but some detailed recommendations for their epoxy primer and Ospho. It can all be read there. Lots of people there here us SPI products and me too, and love their stuff.
I have a 62 Dart (Yes B body) that I picked up. Had no paint on top side and lots of surface rust/pitting. I used the Ospho on the top side and I must have not neutralized the deck lid. I epoxy primed it , and to be honest I forget what I used, it old have been SPI, TCP Global, PP or Kirker. Then it got high build urethane and on the lid maybe polyester primer. Sealed with epoxy primer an topcoated with single stage acrylic .
6 months later, I have some "pimples" show up on the lid. I will sand it back down and start over on it. No bid deal, but things can go South and bit you in the butt!!!
I like the Ospho especially to kill rust in pitted metal. But it needs to be neutralized and cleaned. My opinion is it is a cleaner not a so called convertor.
I needs to go on metal very wt, and remain there long enough to work. I definitely needs to be removed from any metal that is not rusted.

I had a 63 Dart-6 years back and had lots of surface rust on just the hood. I DA'ed just the hood and put a good coat of Ospho on it and it sat 24 then I wiped it down and applied a heavy coat of Rustoleum with yes, a foam brush! I would not touch it for 6-7 month and it sat outside. I wanted to see how it how seal and hold up.
First thing I noticed was I had a wrinkling of the enamel in a few small places. After it had dried maybe a week, I tried to DA those wrinkled places down with the DA and 80 grit. I could hardly touch it! ha When I got back to this car7 months later, the Rustoleum had faded, but it was stuck n there very good! I epoxy primed over that and continued on. 2 years later all was good. It was an experiment.