[orost]

An air-breathing jet engine doesn't need to carry oxidizer, which in a rocket is most of the propellant weight. It also has access to unlimited reaction mass, so it can be much more energy-efficient in producing thrust (it is more efficient to produce thrust by accelerating a lot of mass by a little, than by accelerating a little mass by a lot, but a rocket can't take advantage of this because it would need to carry all that extra mass. A plane can use ambient air for this purpose)

This all adds up to a plane needing to carry many times less mass to gain the same altitude and speed as a rocket, at least within relatively dense atmosphere.

[foota]

Is there a reason that there isn't a stage 0 to rockets that takes advantage of these properties?

[orost]

A rocket on a typical orbital launch profile spends less than 60 seconds in air dense enough for jet engines to have good performance, so there is little to gain.

Pegasus is an orbital rocket launched from an aircraft, but it doesn't exactly impress with performance or cost-effectiveness. Just doesn't make much sense to operate a huge aircraft and design your system around it just to improve on the least important 10% of the flight.