I don't know enough about turbines, so I will happily defer that there are added benefits by going higher for these propulsive systems.
But.
Here's a specific reference saying that
endurance is independent of altitude even for jets. Only max range benefits from higher altitudes as TAS goes up. So, I was half right since we were talking about endurance initially. My mistake was that I though they both were independent of altitude.
Aircraft Performance - Maido Saarlas - Google Books