On an expendable rocket, every bit of inefficiency is more engine, tank, and structure that you have to rebuild for each launch. You want to minimize that. It's also extra fuel, but relative to the total cost of a launch, fuel is essentially free.
If you can reuse the rocket, then that becomes much less important. Maybe you spend 10-100x more building engines and tanks and structures than you would if you had a more efficient design, but you get to amortize that cost across many launches, so it's much less important.
Reuse is, of course, a big if. A gigantic if. The gigantic-est of all ifs. The big question is, "will it work?" If the technology simply doesn't work, or if it "works" to get to orbit but requires so much refurbishment that it's basically like building a whole new rocket each time (see: Space Shuttle), then it's not practical. But if it does work, then who cares if you drag 10x more mass to orbit than you strictly need to?
I am very much in a "I'll believe it when I see it" mode with Skylon, but to me the objections center around the the hard work of going from theory to practice, and the lack of visible progress with same.
A craft that is 100 tonnes dry mass and delivers 20 tonnes payload needs enough fuel to boost 120 tonnes in the last part of the flight. A centaur upper stage by comparison has a mass of just 2.2 tonnes. So for most of the flight you need much more fuel to boost the same payload.
At some point on a degrading performance curve, you don't reach orbit at all even with zero payload.
* The wings would only be useful at relatively low speeds and then just add lots of mass.
* Wings that are efficient at high mach-numbers would be less effective at take-off. Presumably lots of fuel would be burned at low speed to make up for this.
* The structure would need to be strong enough to function whilst horizontal and filled with fuel.
* It would need a large heavy undercarriage capable of supporting the entire take-off weight.
I am unconvinced that horizontal take-off has much benefit anyway. A flight within the atmosphere to a launch site would inevitably use lots of fuel and eliminate any payload capacity. Also, it is hard to believe that anyone is going to allow a massive hydrogen fuel tank to fly over populated areas.
A more traditional single stage to orbit would make more sense IMHO.
You do still need hydrogen etc, but maybe you can bring that in with a normal jetliner.
You always drag engines of the last stage all the way to orbit. More, with a single stage to orbit the last stage is the first stage - and SSTO isn't quite considered an always loosing idea. More - Skylon has advantage of launching only with fuel - and for rockets oxydizer weights several times more than fuel.
Are you sure the drawback you're referring to is actually a drawback in comparison to what the industry have?
1) Skylon has air breathing engines. Air at sea level is about one thousandth the density of normal rocket propellants and thus the machinery for compressing that air (inlets, spinning compressors, in Skylon's case heat exchangers) is large. Air breathing engines need to be much larger than pure rocket engines of equivalent thrust, and thus heavy.
2) Since it's the first stage engines, they are large because of that. SpaceX for example has nine engines in the first stage while only one engine in the second stage. If we assume 500 kg per engine, 8 engines saves 4 tons. Since their payload is about 10 tons, they would only have about 6 tons of payload if they flew with all engines to orbit. (Not a very precise calculation I admit.) Why would they do that? And that's with rocket engines that have 150:1 thrust to weight ratio. Modern operational air breathing engines have about 10:1 thrust to weight, one fifteenth of Merlin 1D.
3) Carrying oxygen isn't as big a problem as it seems to be. It's denser than water so the tanks are actually small. And rockets already have tremendous thrust to weight as we have demonstrated.
1) I fully agree that air-breathing engines are heavier per unit of thrust. Merlins - pretty good rocket engines by that parameter - lift, as you say, 150 times their weight; for air-breathing engines it's 5-10.
2) Aircraft engines usually don't need to be particularly thrusty; wings generate lift, so you can take off even with T/W < 1.
3) Liquid oxygen has density about 1.1 that of water. Kerosene, in comparison, is about 0.8. Difference less than 1.5 times, but the mass ratio is more like 2.5:1, so ditching oxygen tanks - especially at the start, when the system is relatively heavy - can save quite a bit. And why engines' T/W is relevant here?
3) My comment was to compare liquid oxygen with liquid hydrogen which is 0.07 of water density, so you get 16 kg of oxygen for 1 kg of hydrogen for the same tank volume. Skylon uses loads of hydrogen. It's those hydrogen tanks that make it so big. Such tanks are also a lot of dead mass to carry to orbit... Also costs probably scale with dry mass, not wet mass.
So the main drawback is not drag but rather weight. Presumably, they've made the necessary calculations and the advantages of breathing air appear to make up for the additional weight.
As a first stage it would make a lot more sense. Then launch a much smaller pure rocket second stage from there. Staging at high altitude with low dynamic pressure should be relatively easy, probably easier than high speed atmospheric flight or re-entry from orbital velocities with Skylon.