Not IMHO a bad idea really. When I was training and flew to controlled
airspace for XC flights it was suggested that I mention I was a student and
they did seem to slow things down a little.

I can see how a uniform way of doing this might be helpful both in
controlled and uncontrolled airspace. Example, "Bumfigle Tower, Cessna
Student 1234A, ...."

From AVWeb

Britain's Air Accidents Investigation Branch (AAIB) is recommending that
student pilots on solo flights be identified by a radio call-sign prefix so
air traffic controllers can take into account their limited experience and
knowledge. The recommendation came from the investigation of a crash on July
19, 2006, that killed a 16-year-old student who had logged 15 hours and was
on his second solo flight. Just before he touched down at Southend Airport,
a controller ordered him to turn left and climb to pattern height so an
overtaking Piper Meridian could land. It's believed he did not reconfigure
the aircraft and apply enough power for the unorthodox go-around and the
Cessna he was flying stalled and crashed a short time later. The four-person
investigation team concluded pilot Sam Cross was put "in a situation for
which his training and experience had not prepared him" after being
"instructed to carry out an unfamiliar and nonstandard manoeuvre," the AAIB
report said. Adding to the mix was the fact that Cross was returning to the
field after just eight minutes in the air because haze was reducing
visibility. His instructor was watching from the ground as the order to
deviate from the runway heading was complied with and he noted the nose-up
attitude of the Cessna before it stalled and spiralled into a park.
Investigators determined the flaps were at 20 degrees, the carb heat was on
and the engine was turning at 900 rpm at the time of the crash. Cross was
the youngest pilot ever to be killed in a plane crash in Britain.