Not really. Orbit is at around 100km high and roughly 17,000mph. Standard jet planes the size of the shuttle would only get you 1/4 of the height and the 1/10th the velocity. And until you add rockets into the equation, a jet engine plane will very much fall short of orbit; they just aren’t capable of hitting the speeds necessary. They need atmosphere to work…but atmosphere means drag.
So instead of having a bi-modal craft, it’s easier to have just one mode of propulsion.
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