Is a pasted strop necessary?

I only use a single razor; if I use a fine grit stone like a Naniwa 12k, would a Chromium or diamond pasted strop even be necessary?

Necessary? No.
I do have a pasted strop and there are only a couple of my blades I use it on.
It is a preference thing, you may find you like it as many do.

It depends, sometimes the Chromium oxide is used to soften an overly agressive edge.

For many years I never used a pasted strop. Several years back, A fellow member Jacques13 kindly gifted me a chromium oxide pasted balsa strop, and once I gave it a try I could never go back.

I always finish my razors on a pasted strop after the stones, or to refresh the edge. These days, I prefer a loom strop for this. It really smooths out the edge and gets my edges to a level of sharpness I truly enjoy.

Need? No. Nice to have? Yes. Even with some fine naturals, some razors benefit from finer paste like CrOx or CBN or Diamond paste. But not all paste are equal or make a difference on all the razors. Be the honer, the steel or the razor, sometimes the edge doesn't come out as you wanted it or expected it to. That's when pasted strop come into play for me. In my view they cover a multitude of sins (be yours as a honer, steel not reacting as expected on the finisher or the making of the razor itself (defect) or combination).

With one razor and a finishing stone like the Naniwa 12k, I would not invest in a pasted strop, until I know that it's going to make a difference in your face. Maybe try it by itself and if it doesn't feel like before, then invest in balsa and CrOx (cheaper). If you like it, then think about a dedicated strop for your CrOx.

If that doesn't do it, send the razor out for honing and start again, until you find the combination your face like, then you know you will not need anything else.

Unless you come back to the forum for some more knowledge and end up trying another razor made of a different steel and/or a new finisher because your curiosity peek. Double O

Necessary no, but I do use it to remove any burs after using Japanese naturals as per Iwasaki's recommendation. It's more bentonite than CrOx. I also use a paddle strop pasted with bentonite clay and Ozuku powder I collected after sawing off a piece for a Tomonagura. This works really well.

Yes. Once you have one you'll wonder how you lived without it.

Not a necessity, but is nice to have. It's all personal preference and I think can depend on the steel of the razor you have. I only own 2 razors (dovo special and a roughly 100 year old solingen razor). I find the antique doesn't benefit in the result straight from my coticule but still use chromium oxide every now and again for a quick touch up. On the other hand my dovo for some reason gets a smoother edge from chromium oxide than coming from my coticule.

I suggest getting some chromium oxide to try it as it's inexpensive to buy, and the only way to know if it has an effect and if you like the edge you get from the pasted strop, is to use a pasted strop. :)

It's another tool to have in your arsenal of honing options. But you have to be careful that you don't use it as a crutch like I did for a while. You can cheat your way to what feels like a shave ready edge by using diamond spray but it's never going to be great. I was convinced that the ONLY way to get a truly sharp edge was with a pasted strop. I was wrong and treated myself to a lot of harsh edges instead of working through my stones. If you're working with one good razor with a good edge on it, I'd say you don't NEED a pasted strop. I would opt for a 10k-12k stone and use it when necessary. When you inevitably end up with more razors and discover the individual challenges that each can present, then you may want to have another option at the ready.

^^^^^^^
What he said is 100% correct.

IMO pastes have their place in a honing arsenal. I will not be parting ways with mine :)