>>14134050I think the idea has a lot of merit - it's just no one has done it. The problem is that it combines the expenses of rocket engineering with the expenses of aircraft engineering, with unclear financial benefits. I think the closest anyone has gotten to a viable system was the Soviets/Russians with their MAKS shuttles, which would've repurposed their heavy lifter An-225 as a carrier vehicle.
I think this could've come online in the 90s.
But anyway, the main advantages of this system are twofold - one, due to how rockets work, they have to accelerate their own fuel, meaning that the deltaV-fuel mass graph is exponential, they expend most of their fuel to get to comparatively low speeds.
The other is that less dense atmospheres allow for bigger, more efficient nozzles, as the exhaust velocity of the propellant can be higher, due to lower atm pressure. That's one of the motivations behind staging.
Pic related was a conservative, and pretty down-to earth first step, even if we consider that the carrier aircraft flew somewhat below Mach 1, and at 30k feet (typical airliner numbers).