Have you ever had a patient deteriorate during transport after you contacted the hospital?
It has happened to most of us and will happen to you at some point. BLS crews may be upgrading their response and calling for ALS to meet them enroute and ALS providers may be pulling additional medications or performing additional skills, but during all of that controlled chaos, please take a few seconds to advise the hospital.
Since you have already contacted the hospital, they deserve a very brief update (as time allows) regarding the significant change in patient status so they can better prepare or alter their response. They may even opt to divert you to a better facility in some cases.
Significant changes might include things like serious mental status changes, new hypotension, cardiac arrest, BVM use, a serious new assessment finding, STEMI, etc.