I like what he brings in terms of team defense and charge taking, and when he's on his game I like how he spreads the floor with his mid-range jumper. In particular I like his ability to score points at a nice rate as long as he isn't dealing with a very unfavorable matchup (though there are a lot of those out there for him).
I don't think there's any doubt that there is a role that Glen Davis can play on a good team -- he just needs to stay within that role.
The problem I see with Glen Davis on this team is that his problems - lack of speed, size, athleticism, shot blocking, rebounding - are all problems with which the starting unit struggles as well. Thus playing him 25-30 minutes a night, with long stints alongside the starters, adds to the existing strengths of the lineup we have out there, but doesn't really shore up any of the weaknesses.
To put it more simply, now that the Big 3 are getting older, slower, and have less energy to expend, if we're going to play a guy off the bench, we need a guy who provides us with things we desperately need: energy, rebounding, inside scoring. Baby doesn't really do that.
Like you said, though, there may simply not be any better options out there right now. Guys like Kris Humphries, who would be perfect for this team, are almost certainly well out of our price-range.