The thing is, the goal of a rocket is not to "lift things off the ground", it is to "speed up things to an orbital velocity" -- around 8km/s for LEO.
From this point of view starting the rocket engine in the air at 0.2km/s speed is a marginal improvement compared to starting it on the ground. It still can be an improvement if executed correctly but it's hard to make it big enough to justify the complexity.
Isn’t most of the speed you spend on the first stage wasted on going up, though? And what little momentum you might get to keep when it’s time to turn into your orbit is also sucked away by air resistance. Rockets have to go directly up for the first part of the flight, and all that acceleration is wasted because what you really need is orbital velocity, which is going to end up being “sideways” relative to earth. An air breathing first stage would mean you have to give a little less of your fuel to going up, and you’re doing it in an environment with less air resistance.
And any gain in the very first part of a flight can also be achieved by just making a cheap rocket first stage slightly larger.
Being able to propulsively recover rocket first stages, as Falcon 9 demonstrated, has destroyed pretty much any rationale for winged or air breathing first stages.
Winged and air breathing first stages are a square peg round hole situation because high altitude and runway technical requirements are so different, and at low altitude reaching mach 0.8 is all you get to do cheaply - a negligible benefit considering the extreme costs associated with either horizontal plane-style integration or high TWR turbines. If you're going to optimize for getting useful delta V out of them, you need to do it in the stratosphere with ramjets/scramjets, which have minimum airspeed requirements on top of the minimum glide airspeed requirements necessary to keep a heavy aerodynamic body from falling to earth. You're best starting out at extreme speed and high altitude by launching from a hydrogen or vacuum filled maglev at Chimborazo or Kilimanjaro, and using the scramjet to get from the summit launchsite at a muzzle velocity of atmospheric-mach 3 up to the Karman line at mach 10. The initial speed provides the ability to go directly to hypersonic engines, the ability to trivially maintain altitude and build speed with only modest TWR and small light wings, and the ability to minimize drag losses by going through very thin air.
From this point of view starting the rocket engine in the air at 0.2km/s speed is a marginal improvement compared to starting it on the ground. It still can be an improvement if executed correctly but it's hard to make it big enough to justify the complexity.