While I will say it's very much up to debate the merits of trading Avery Bradley, I do think that we all need to be realistic here.
Unless Phoenix is feeling ridiculously generous, it's going to at least take Avery Bradley, a good player with salary (Bass likely), and a sweetener like Melo, Sully or a pick to get this done.
Gortat is a legitimate NBA center averaging 11, 9, and 2.5 this season. And he's arguably being underused in Phoenix right now.
You don't get a player like him by giving up a package of role players and second round picks.
Personally, I'd do it. As others have pointed out, Gortat is only 28, so he's going to be good for at least 5 more years (and likely more). With he and Rondo secured, we'd have the two toughest positions to get quality players covered.
I'd really miss Bradley, but you have to give up something to get something.