Just skiming through the"Official USCF Rules" book, 7th Ed., updated,

I couldn't find anything that specifically prohibted it, although the book makes clear that Blitz ratings and Regular ratings are different. Also, lots of fudging about how things can change over time, etc. Googling will quickly yield the answer that only classical or standard time controls can count towards any title under the control of FIDE and (I think) under USCF as well. Dubiously, many of these Google hits come from Chess.com.

I suppose you could post the question on Hikaru's You-Tube channel, he ought to know.

Is it possible to become a national master by playing only blitz?