Editorial rejection: should I write back?
No doubt your first instinct is to challenge this desk rejection, but I would advise against it. 

It is well known that appeals rarely succeed when referees go against you. When a handling editor thinks your work is not sufficiently interesting, I'd say an appeal is even less likely to be successful.

Coming specifically to Phys. Rev., your situation is somewhat worsened by the fact that alternatives to the Phys. Rev. A-X stable are not as attractive or popular. 

But if your work is sufficiently useful, and helps advance your field, it will get cited even if you take your paper elsewhere. There is evidence for this in your case: You have senior researchers on arXiv giving you good feedback.