I can't believe it's nearly as common as it was 5 years ago. It's anecdotal, but all of the big IE-only industry-specific web apps I've had contact with have been rebuilt.
There certainly are some in the wild, but Microsoft doesn't need to have support for these old applications hold back progress. They certainly can (and do) have separate modes within the same browser, they could even run separate engines. They could also just distribute a separate "Legacy IE" application to support these apps.
But that's one of the many problems with Microsoft: they refuse to make hard decisions.
There certainly are some in the wild, but Microsoft doesn't need to have support for these old applications hold back progress. They certainly can (and do) have separate modes within the same browser, they could even run separate engines. They could also just distribute a separate "Legacy IE" application to support these apps.
But that's one of the many problems with Microsoft: they refuse to make hard decisions.