To compound on what Fafnir and maybe others have said,
What buyers are going to be out there for Bradley that can afford to give him more than the MLE? Are there any teams that would sign him and insert him as a starting SG?
The No's (don't need to read, this is me doing my research)
Lakers? Obviously no.
Toronto? Not with Landry Fields and Derozan at SG.
Washington? Not with Beal at SG.
Memphis? Small possibility but very unlikely. Would need Z-Bo to opt out to have enough room. Is Bradley an upgrade over Tony Allen?
Golden State? No way, will need a center.
Dallas? No, Ellis seems to be working out there at SG.
San Antonio? All set at SG. Only would sign him on a bargain.
Orlando? Already have a few quality SGs and I think are looking for that superstar player.
Sacramento? I think they want to give McLemore a real shot as their franchise SG.
Phoenix? I don't see them letting go of Bledsoe this offseason, but this team could go a number of directions this offseason.
Milwaukee? I can't see them spending that cap space on a role player without a go-to guy in place.
The possibly's
New Orleans? Interesting! They have their star player in place (Davis) so don't need cap space for that. I think Bradley would be a very nice complementary piece next to Holiday in the backcourt. The problem is that they have Gordon signed at SG for a lot of money. If they believe they could move Gordon, I think this would be a sensible signing. SF is their more pressing issue right now though.
Detroit? Possibly, SG is the weak link in their starting lineup. Their management tends to be rather unpredictable.
Cleveland? Possibly. That roster seems to be full of unfitting pieces in need of a total makeover. I don't see them giving up on Waiters this early though.
Charlotte? Possibly. I think they will be looking to go after a more marquee player with that cap space, but another team that is managed somewhat unpredictably.
Atlanta? Another possibility as Korver can slide to SF. I think they only do it on a bargain deal though.
Utah? A wildcard possibility as they'll have a huge amount of cap space. Who knows what they'll do if they don't get the chance to spend it on their target players.
Philadelphia? If Turner lasts past the trade deadline, I think they might let Turner walk this offseason is the price is too high, in which case they could sign Bradley. MCW's height at PG could help cover AB's height at SG.
Summary: I think the Celtics do need to be concerned that at least 1 team from those possibly's could offer Bradley $7M per season. I think that may be too much for the celtics to match with his limited ceiling and no real plan to contend in place. I'd match anything at the MLE or less.