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Its hard to say Frank,
The problem with getting a little boost in speed out of the same amount of fuel(less pumping energy) you create a little more air in the intake(ram scoop) and then burn a little more fuel.
In Turbine engines you get runaway caused by the increased intake speed increases combustion energy increases compression, increases combustion. . .and so on and it. In a turbine driven engine its a big deal. . .reciprocating. . .not so much because there is only so much pumping loss to overcome.
Its going to be a small improvement with a ram scoop, but there theoretically is an advantage so long as you don't lay into the throttle too hard with the added power. That said. . .it is a real improvement opposed to a "restricter plate" WAI.
And no the air density influencing the engine has nothing to do with why the run at altitude. Its a calculus maximization problem. The higher you go the crappier your turbojet engines work, but you get ALOT less air density. They go to 30+ thousand feet because at that altitude the radial compressor at the front of the turbojets can still supply enough compressed air(If theoretically they could run the engines at sea level and the aircraft at 30K feet they would) to make the turbines push enough.
If you think I'm wrong. . .ramjets are turbojets which let the compressor "runaway" and compress the air to the limits of the housing. Then it has a giant scoop to force feed air into the engine. They are actually more efficient than regular jets.
The only problem is. . .you have to piggyback them up to mach 1.5 or so and then drop and engage them. It costs a ton of fuel to launch and so its not viable but a WAI and less air in the engine blah blah blah. . .its a restricter plate, look it up under NASCAR.
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