Only if going through with the kill would actually hurt someone.

[ He lifts a hand to punctuate his points, getting more animated now. ]

Because think about what leaving him alive would mean for the story: Bromfred eventually escapes, then snitches on Ebegeeser. Even if Bromfred didn't actually have visual confirmation that it was Ebegeeser, he'd probably raise a stink and make Ebegeeser suspect number one. Killing Bromfred is way tidier if you think in the long-term.