I have a handful of sites running ASP.NET 4.5. Migrating them would cost an unknown amount of time and require substantial rewriting of major components (such as all data access). It might not even be physically possible to do, given dependencies on libraries that are still 4.5 only.
It sounds like it would also kill our build process dead (adding another major rewrite to the tally). And of course, it would leave us reliant (correct me if I'm wrong here) on a lighter weight version of VS.NET so we'd roll back the clock about 10 years on ReSharper-like goodness.
As reward for this, migrating over to Core would gain me roughly $0 in business value.
The alternate course is to stay with 4.5 for as long as possible, eventually moving across when Microsoft decide to VB6 it.
Sounds like a plan.