Variable shape expansion nozzle

I just had an idea. It probably wouldn't work but I was wondering
if anyone had thought of it, and found why it doesn't work.

The ideal shape for an expansion nozzle isn't the same at sea
level as in vacuum. In fact there has been some rocket engines
which would extend the nozzle when a given altitude was
reached in an effort to always have a nozzle shape which is
nearly optimal.

My idea is to build a nozzle that has a shape optimized for
vacuum but to add inside something that fills in some space
to make it look like a nozzle optimized for a pressure of 100 kPa.
The filler material would be made of something that melts
at just the right rate when the engine is on. Or maybe even
something that burns at the right rate, something like the
solid fuel of solid rocket motors might do.

You get a nozzle that is optimized for 100 kPa at launch
and optimized for vacuum when in vacuum. With the
additional benefit that the walls of the nozzle are protected
from the heat for the first few minutes.

Of course there are a few technical details that would
need to be taken care of before implementing :-)

Alain Fournier