The idea of Skylon was to not have to carry and accelerate the oxygen that would have been used by a first stage. It makes the beginning mass lower and allows for more mass to orbit than a regular rocket, the kind of rocket that is limited by the tyranny of the rocket equation.

It would have been nice to see whether Reaction Engines could make it work and how economical it would have been. This is the beauty of having so many companies trying their own solutions. Not all of them will work, but they may make progress into the impossible. SpaceX has done the impossible a few times in the last two decades, and it would be nice if someone else could also perform miracles.

Lets say a Falcon Heavy is used to launch an orbiter and throw away second booster.

The orbiter needs to have reaction jets and fuel to help dock with something else in space.
It also needs to have heat shielding to get back into the atmosphere.
It also needs to keep enough fuel for air breathing jet engines to keep it flying for 30 minutes.
It also needs a large enough jet engine to provide enough thrust.

This is only if you insist on the orbiter actually flying at some point and not just gliding.

Or go the other way and have a carrier plane that gets you to about 300 thousand feet and drop off a rocket to reach orbit. How big would that rocket have to be to reach orbit from that speed and altitude. HUGE!. Your carrier plane is only saving the first 300 thousand feet and 1000 miles per hour. A drop in the bucket.

Apollo back in the day proved we could re enter a capsule with good one mile accuracy. Space X has proven we can directly hit a target within a few feet. Why fly to our eventual target landing area? Wings are no longer needed. They are just wasted weight along with air breathing engines.

Oh God, where to start?

The rocket equation makes SSTO barely possible for a purely rocket-powered theoretical vehicle with no appreciable payload-to-orbit capability. Having barely reached LEO, an SSTO would then be tapped out and would have no source of propellant to refill its tanks so it could go much of anywhere else. Propellant depots supplied from the ground by fully-reusable TSTO brute lifters would get around this limitation – that is, after all, part of SpaceX’s Starship architecture. But, if one has a perfectly serviceable fully-reusable TSTO brute lifter, of what real benefit is having a far more expensive, complex and also vastly less lift-capable SSTO? The question answers itself.

And even that scenario posits a pure-rocket-powered SSTO. The whole Skylon concept introduced several additional hurdles to overcome – apparently Earth’s gravity well having been an insufficient challenge.

A combined-cycle engine that can be a jet in sensible atmosphere and a rocket above it does not relieve a designer of the necessity of carrying tons of liquid oxygen if the vehicle is intended both to reach orbit and have some way to come back. It merely shifts the burden of producing that LOX from ground systems to on-board systems – pretty much the opposite of SpaceX’s engineering principles, to wit “the best part is no part” and the off-loading of every possible function to “stage zero” and not the vehicle.

Then there’s the dry mass of the vehicle to consider. Making LOX in-flight requires not only a flying LOX plant but a heat sink into which to dump the heat generated by compression of ambient air. On Skylon, that was to have been the extremely cold LH2 fuel. LH2, unfortunately, has quite a low density, requiring very large tankage which, in turn, increases the dry mass of the vehicle. And Skylon needed to carry enough LH2 not only to burn to putatively reach orbit, but enough additional into which to dump the heat of liquefaction of the LOX. Just densifying ambient air would be tough enough, but an actual phase change is needed to liquify oxygen while not doing the same for the propulsively useless, yet dominant, nitrogen fraction of Earthly atmosphere.

And then there’s the putative “ceramic-metal composite” airframe material which was to have done double duty as structure and TPS. Color me skeptical – even with a buttload of LH2 aboard to act as a re-entry, as well as an ascent phase heat sink.

The whole Skylon notion had much in common with Ptolemaic cosmology in that Ptolemy tried to save a fundamentally incorrect concept with multiple layers of epicycles while the Skylon vehicle design required multiple layers of subsystems that purported to fix the problems introduced by the next-lower layer of subsystems.

It does not have to carry the same load as Starship in order to succeed. It would fill a niche that Starship, Falcon, New Glenn, and Vulcan don’t. More is not always better, although many people seem to think so. ISS and other proposed space stations do not need to be resupplied with 100-tonne payloads, and they do not need 100-passenger shuttles.

Reusable first stages may make things less expensive than expendable, but as a reusable SSTO vehicle, Skylon would have a reduced complexity of operation and would have the possibility of even greater reductions in operating costs.

The main technical development that was needed was the engine, which would transition from air-breathing to on-board oxygen. One advantage would have been that the craft would not have to carry several tonnes of LOX, reducing the overall fuel need, size of the craft, and weight of the structure. Notice how much larger first stages are than the upper stages, yet these first stages tend to take the upper stages only around 1/5th of the way to orbit.

Buran actually was to have landing jets where we put the OMS:
https://www.secretprojects.co.uk/threads/energia-buran-space-transportation-system.5656/page-6#post-719399

A mix of these concepts means an orbiter, after re-entry, is just another airplane with run-of-the-mill jet engines—no advanced airbreathing engines.

The RAF should have funded SABRE

Something with just enough engine to give it a better than one shot at landing like the shuttle had.