David Tennant isn't my all time favorite, however in my opinion he is in the top 3 or 4 Doctor Who actors.
It seems to me that the way the writers brought him back & left him on Earth in parallel to the current Doctor may have been on purpose to possibly bring him back for a recurring role.
I say bring in some hype by actually killing off the current Doctor, leaving Tennant to pursue the task of defeating who killed him & then on to thwarting evil in further adventures. It can start off by him being on Earth for a few decades to explain the aged appearence of Tennant.