Getting a BB job just for brand name?

I'm an incoming analyst at a MM. Been in NYC for a year prior, and plan to stay in the NYC area for 3-4ish years before calling it quits on the city. Theres a few things I noticed, that at my previous role (NYC-based) I was getting more hits for interviews and HH inbounds than my colleagues an hour away in the exact same role and felt much more negotiating power/desirability when looking in different cities. Now I upgraded my title and expect a meaningful bump in that same status. Provided everything seems fine and theres no red flags I plan on staying at my current firm and even transferring to a regional office in my hometown when I decide to move. But the thought crossed my mind, since career progression is a game of increasing closing doors, that would it be worth my time to get one last hoorah at a BB for like a 1 year stint as an 1st or 2nd year associate solely for the branding? Another idea was seeing if I could join a GS/MS/JPM (not EB), in an adjacent role (AM, IR, Strategy, CorpDev) to then introduce myself as a ex-GS professional. Note, my (hopefully) next steps would be 1. LMM PE/GE, 2. Venture (Corporate or Independent Fund), 3. Chill Corporate Dev/Strat + founder combo, all at a T2/T3 city. One big data point I have to back the brand-name thought is my old bosses were both MF/BB directors in non-FO seats before pivoting out to entepreneurship and no one questions their abilities or credentials. I plan to continue updating my title, but my question is, is it worth it to go to a shop like that solely for brand name/credentials/network?