I would probably say U2 was the band of the 80s.
At first, I thought of Culture Club ( / s ), but then saw your post and agree.
Given the "flash in the pan" phenomena that is modern music, I'm not sure we'll be able to name "decade bands" beyond the 1980s. There may be 5-year periods, but that's about it.
90s - Pearl Jam
00s - White Stripes