Bornstein seems less likely to be a mass prescriber to me, just based on my experience dealing with some.
I can only go into a few reasons.
If Bornstein were a Dr. Feelgood, I think someone would have already come forward. People will rat out people if it involves tRump. Look at how long it took Dr. Ronny Jackson to get outed.
Also, Bornstein would be even nuttier than he appears to be. He would have to be suicidal. If Bornstein had been handing out scripts and he then tells this story of the raid, he would be demanding to be destroyed. He knows firsthand from the raid that tRump is a vengeful monster. He might as well have asked the DEA to take his prescription pad and lock him up. He is now going to be facing scrutiny that no one who was routinely breaking the law can survive.
There are also better and easier ways of prescribing controls than using a pseudonym. (Those ways are still illegal but safer.) And keeping records associating the real patient with the pseudonym would be epic stupidity if controlled drugs were involved.
A more likely reason for prescribing to a patient using a pseudonym would be prescribing embarrassing non-controlled drugs. For example, if Bornstein prescribed Viagra, Propecia, an antidepressant, a mood stabilizer (like lithium), or even Glucophage for diabetes. This is still illegal but less likely to result in loss of a license.
Now, I'm not saying it's impossible that Dr. Bornstein prescribed using a pseudonym for prescribing controls, just less likely than the pseudonyms being used to keep embarrassing labs and tests private. Still, Dr. Bornstein could be a Dr. Feelgood, nutty as it would be. Anyone associated with tRump seems to be nuts to some extents