I offered my whole theory on Brenner once before that I think explains his whole motive thing and I'll do so again. To me, the key to understanding him is his remark, "I find it dull," when Columbo acts in awe over the opulent lifestyle he leads where he has anything at his disposal. Brenner goes to the trouble of inventing Steinmetz, confounding his own bosses at the CIA and in effect screwing them, not because he has any traitorous impulses, but because to him, it's all a giant thrill that he does just to see if his brilliant mind can do it.

Brenner is ultimately a lot like the title character of the Steve McQueen movie "The Thomas Crown Affair", a guy who has it all and should be able to enjoy his life, but who plans a heist just because he wants to show he can beat the system. So too is it of Brenner in why he invents Steinmetz and engages in this whole game to begin with.

I would add that Steinmetz, when expected to be a suspect, would be an impossible person to find...being non-existent.

Hey Hey: Steinmetz...Thomas Crown....Faye Dunaway...Chess Game....but finally checkmated by Columbo. Which kiss did Faye Dunaway like better? T. Crown or Columbo ?