Was having this discussion with my wife earlier. Here are a few bands who I think could have done one.
1. Fleetwood Mac (although they're still in such rude health they probably still could)
I can't say that I'm all that surprised by the fact that they never did one, although I would have loved for it to have happened (and would still welcome it, for that matter). I think the main obstacle there would have been that, first, the band would have never been able to agree which of them would be the lead vocalist on something like this. I can only imagine what the behind-the-scenes arguments between Nicks and Buckingham would have been over that issue. I'm not sure that Nicks' Mac material would have been suitable for a Bond theme, as that body of work is usually very deeply personal and revolves either around her drug addictions (see Tango in the Night and "Gold Dust Woman" as an example) and more mystical themes ("Gypsy", "Rhiannon", etc.), or the music is not-so-subtly targeted directly at Buckingham (Rumours, and various other songs over the course of the band's six albums). I think by the time that they would have been a viable option for EON (which probably would have been for The Living Daylights), it would have been Buckingham that would have been the more logical choice to contribute the track, given that he'd already contributed a film title track by that point ("Holiday Road" for National Lampoon's Vacation) plus the fact that his sound would have been a better fit for the direction EON was going with the title music (a-ha for TLD and the initial interest in Eric Clapton for LTK).
That all said, the band could probably still pull one off.
2. The Eurythmics (would've been PERFECT)
Kind of surprised that one never happened. I'm not particularly a big fan of the band, but it would seem like they would have been a good fit for Bond.
5. Madonna (yeah OK, I know she did eventually do one but I'm still surprised it wasn't done much earlier)
They definitely went in this direction far, far too late. Madonna circa "Open Your Heart" would have produced a much better title track than what she gave us for Die Another Day, which unfortunately happened to coincide with her foray into more electronic-driven music.
9. Oasis (would've seemed a dead cert in the Brosnan era)
Certainly would have been a better choice for the title track for Tomorrow Never Dies.