It's easy to vilify the guy. He did a lot of dumb things. But I would never want to deal with the pressure and expectations of being GM of a team immediately after a World Series win. I would never want to be a GM, period, but still. The new GM will have so much more of a clean slate.
FWIW, I supported the Ryan Howard extension at the time. One of my fondest memories of the Amaro era was when they added Cliff Lee, leading to the "H-O-H-Lee Shit!" season. The subsequent postseason was the most depressing.
They have to get a new field manager before they get too far into the offseason, they'll want to have the new GM hired to be part of that discussion, and so they can't wait until the season is over to make that move.
Plus, this seems like the best time of the year to get a hold of GM candidates. Minor league regular season ended on Labor Day, there's no more player movement for now, and you can't do a lot of deep planning for next season yet. September is nerve racking, but there's probably not a lot to do if you're an assistant GM or scouting director.
...Is being able to hear all the other announcing teams around the country. I was watching the Dodgers/Padres last week and I gotta tell you, it was really cool to hear Vin Scully again after all these years.