Just off the top of my head, guys that are still in the league and have been able to stick around for multiple seasons with similar post-oriented skills: Nikola Vucevic, Jonas Valanciunas, Alex Len, Andre Drummond, Robin Lopez (not Brook), Steven Adams, Rudy Gobert (not, repeat, not implying that Edey will ever have his career, but similar size and offensive/defensive range), Nurkic on the Blazers; even Boban has stuck around for almost a decade.
Even the ones on the list that have started to add a few perimeter shots to their arsenal, like Vucevic and Valanciunas, definitely didn't have that their first several seasons, and continued to stay employed. It's certainly not the norm, but big men like Edey are still usable. I'm not guaranteeing he'll get drafted or 100% will find a roster spot, but it's not out of the realm of possibility that he would, either.