Here's the challenge with using Romex as power cord. What I have found through testing and experimentation is that the frequency response of your equipment is definitely affected by awg of solid core wiring of your power cord. I have built multiple power cords using different size conductors (16awg, 18awg, 20awg, 22awg). In all cases, I braided the conductors for hot/neutral/ground. All power cords had multiple braids which equated an overall size of 12awg for the power cord itself. I have found that with larger awg conductors (such as 16awg), I actually lost high frequency response. 18awg was okay, but with 16awg the sound started getting very "low fidelity". Also, there was a blare/smear in the midbass/midrange (likely because of skin effect on the large 16awg conductors).
When I went to using 22awg, I found that I had way too much emphasis on high frequencies and I lost power in bass/midbass. I actually found that 20awg was the perfect center point where I had enough bass/midbass power and still enough high frequency response.
If you choose to use 12awg or even 14awg romex for your final power cord, I think you will suffer in the results. Most power cords are bundled stranded copper, with high amount of tiny strands (likely 28awg or 32awg strands). I never had good results with stranded power cords, even using the ultra high grade OCC copper Furutech power cords. It just didn't sound right.
That's why I like Audioquest as a power cord material. They typically use 21awg for HOT conductors and 19awg for NEUTRAL conductors. And it's always solid core conductors (except for their cheapest "X" series). It's a good mix that averages out to my "20awg sweet spot".