If we draft Byfield, Brown doesn't become immediately dispensible, but in a year's time he does. Assume Byfield gets sent back to the OHL, Brown could take over regular duties in Ottawa. Just the sheer number of centers ready to play in 2021-22 will force the hand though (Byfield, Brown, Norris, White, Tierney, etc.) I doubt Norris is getting traded. It may come down to White/Brown, and White fill more of a need than Brown does IMO (defensive specialist, PK, projected replacement for Pageau). Tierney likely will be trade bait as well. Whatever Brown can do, Byfield can probably do better.
EDIT: there may also finally be a realization that Logan Brown is just too injury prone. He's battled it pretty much his whole career, would be foolish to think it will suddenly turn-around for him