The biggest problem is that you wold then have to carry an engine system that you use only part of the time. For example, if you have a dual jet-rocket system, you use the jet to the upper limit of its usefulness, thenswitch to the rocket, unless you jettison the jet engines, you are still carrying them with you, and this adds to the cost of getting nto space.
Conversely, if you use a two step approach, say a very carefully designed supersonic jet that lifts the rocket to the jet's outer limit of operation, then the rocket 'plane' only has to carry the weight of the rocket into space.