The first stage of SpaceX's Nov 18 Starship launch was the Super Heavy. According to the Wikipedia page, it packs 3,400 tones of fuel. In the launch video, it shows the rocket reaches 27 km of altitude at 2600 km/hr at t+01:44. The engines start turning off at 02:40. Assuming a constant rate of propellant consumption, the first stage spends about two thirds of its 3,400 ton propellant to get out of 1960s' SR-71's flight envelop. With similar analysis, it got out of A380's flight envelop at 6 km altitude and 950 km/hr at t+00:50, after spending about 31% of it's propellant.
Turbofan engines have a specific impulse 6-20 times more than rocket engines. The exponential relation in the rocket equation means an engine with higher specific impulse would greatly benefit in cost, weight and payload. In addition to having better specific impulse, airplanes need much less thrust than rockets for the same payload because the engine doesn't have to directly lift all the weight. Jet engines are just as complex as rocket engines, if not less, but arguably more mature as a technology.
In this scenario, a space launch system that uses a specially designed airplane as the first stage and rocket engines for later stages may save a lot in fuel and weight while not adding much complexity. The first stage will be reusable by design. For private space companies like SpaceX, that have drastically cut costs for launch and operations, and designed all of the rocket system on their own, this approach looks worth considering. This is different from projects like SABRE. What I mean is a totally airplane design, horizontally thrusting jet engine and wings providing the lift, much like the Pegasus project but with a specially designed first stage instead of a commercial plane.
What is the largest barrier to using launch system that has an airplane as the first stage and rockets for later stages?