This land-on-tail stuff is thrilling Buck-Rogers era, but it's literally a waste of oxygen.
Of all the things you could waste in rocketry, oxygen is probably one of the better picks. Oxygen is wonderful: it's dense, it's very cheap, the tanks are light, and you throw most of it out the tailpipe so it isn't part of the dead mass carried into orbit. On the other hand, replacing the rocket engines (with 100:1 to 200:1 thrust-to-weight ratios) with an airbreathing engine that might optimistically have a 10:1 thrust-to-weight ratio means you're hauling more deadweight into orbit. You need a more aerodynamic aeroshell and heat shield, which means it has a worse surface-to-volume ratio than a simple oxygen tank and thus more weight. You need more elaborate aerodynamic controls and landing gear for the aircraft-style performance.
Worse, the stuff you're keeping with these oxygen-saving airbreathing engines is probably hydrogen. Hydrogen's a headache: it has very low density, so its tankage is heavy compared to oxygen, and it's a pain to store, insulate, and handle. Everything associated with hydrogen is heavier than denser fluids: heat shields have to be larger, engines have lower thrust-to-weight ratios, the tanks are bigger and thus heavier, etc.
A glimpse of the value of dense fluids is seen in this comparison of hydrogen-oxygen and kerosene-oxygen SSTOs (end of the email chain has plenty of detailed numbers and engineering discussion).
So, like I said, oxygen is probably one of the best things you can waste in rocketry.