The Police are precisely the band I had in mind when I wrote that. U2 in March 1988 were at about the same place the Police were when they broke up after the end of the Synchronicity tour in March 1984. Synchronicity sold over 11 million copies that year making it the biggest selling album by a band worldwide in 1983-1984. The Synchronicity Tour also set attendence records, Gross Records, and fastest sellout records around the world. The Police were nominated for 5 grammy awards for Synchronicity and won 3 losing out to Michael Jackson for Album of the year and Record of the Year, but picking up Song of the Year, Best Pop song by a group and Best Rock Album by a group. U2 in March 1988 had sold 14 million copies of Joshua Tree Worldwide and won one of its two Grammy nominations, the one being for Album of the year. The Joshua Tree tour was huge and broke new records.
Although musically different in many ways, both bands had just completed their 5th album at these respective points. Both albums Joshua Tree and Synchronicity were big evolutions from the style and sound from the first albums Boy and Outlandos D'Amour. The first and 5th albums sound like two different bands.
One difference is in the amount of time between the release of the first album and the real and hypothisized break up points. For the Police the first album was released in November 1978 and their break up occured in March 1984. For U2, Boy was released in October 1980 and the hypothetical break up occuring in March 1988.
The Police were just inducted into the Rockin Roll Hall of Fame and I am confident that U2 would still be inducted into the Hall of Fame at their first chance even if they had broken up in March 1988.
As far as what Bono and the Edge would have done, if they had broken up in March 1988, I am not sure. Even more interesting would be what Larry and Adam would do.
As it stands, the Police are the only band that the above senerio has happened to that I can think of. Their last album and tour were their biggest and most critically praised and barring a few live appearences they have never gone back and done another album or tour, yet.
It is strange to think of U2 without all the albums and things that have happened since Joshua Tree. Despite the Criticisms of Rattle And Hum, that movie brought a lot of young fans in who were to young at that time to go see them in concert, but were able to get to the local movie theater.
I'm thinking if U2 had broken up in March 1988 they would have still put out a concert show from the Joshua Tree tour, just as the Police did for Synchronicity. Rattle and Hum was a documentary though that had new songs, so it would not be the same.