>After shutting the inlet cone off at Mach 5.14, and at an altitude of 28.5 km, the system continues as a closed-cycle high-performance rocket engine burning liquid oxygen and liquid hydrogen from on-board fuel tanks

the benchmark of today - SpaceX - separates the first stage at Mach6-8 at 65-80km height. Thus, the SpaceX second stage has less delta-v to add and don't have to carry all that weight - the SABRE would naturally be bigger than the 2nd stage for the same payload. The economical space related case of HOTOL/SABRE single-stage-to-orbit pretty much disappeared for a foreseeable future when SpaceX started to recover the 1st stage. That not to say about suborbital flights SF-Shanghai though. Or even "just" hypersonic as SABRE tech seems to successfully deal with one of the major/key obstacles for it (and that is huge, i'm in no way trying to dismiss their work). And one can see how SABRE can be used in some cases as a convenient 1st stage, i.e. by being able to launch from any big airport instead of only specially designed spaceports (such a 1st stage would probably be better than that https://en.wikipedia.org/wiki/Pegasus_(rocket)#Carrier_aircr...).

Mach 5 at 28km and mach 6 at 70km are not all that different. Mach slows down with altitude. And specific altitude numbers dont matter much if you are aiming for orbit. All that really matters is horizontal velocity. The first stages of both schemes are relatively slow. Both get the bulk of thier orbital velocity from thier second stages.

SpaceX takes a very non-aggressive approach with its first stages. When they detach they arent moving nealy as fast as other rocket first stages. That is done so they dont slam back into the lower atmosphere but it means relying upon second/third stages to do the horizontal work. By the raw physics, it isnt the most energy efficient approach. It is a compromise to facilitate recovery.

Imagine putting SABRE on the first stage though - the engines would be heavier, but using air instead of carrying oxygen, for the full burn of the first stage. The payload mass fraction would be dramatically higher without carrying the oxidizer mass on board.

It is possible though cost&complexity seems high - we theoretically can even today bundle a bunch of SR-71 engines and probably stretch them beyond designed Mach 3.3 for the short time. Having low thrust-to-weight (SABRE promises up to 14, SR-71 had 6) we'd need either a lot of them for VTOL which leads to high cost, or we're limited by the size of maximum realistically possible hypersonic capable plane, plus the plane body being the additional weight. For example VTOL calculation - say engine weights 1 ton, we can lift off 13 ton of fuel and payload. It will use 40 ton of O2 from the air. For rocket engine - 1 ton engine can lift off 100+ ton, and if we just take the 13 ton fuel plus 40 ton O2 we'd have 45 ton budget for the rest (body plus payload). In reality you'd need higher fuel ratio, and this is why VTOL for atmospheric breathing engine pretty much isn't an option .

Going beyond pure rocket engine for the 1st stage i think air-augmented rocket (http://astronautix.com/g/gnom.html) being simpler (thus cheaper) would be the next step that would get us closer (specific impulse wise) to what SABRE is targeting.

I think one of their big advantages over SpaceX is noise pollution. Nobody is going to be launching Super Heavy near significantly inhabited areas just because of the noise.

I think the benefit of launching horizontaly is overstated. Any airport would still need to handle LOX and hydrogen which could be pretty dangerous. And the airport is not necessarily going to be in the right place for launch.

Also traditional rockets have most of the forces acting vertically. A horizontal launch space plane must also deal with a completely different set of forces.

One might argue that a 3km runway is harder to obtain than a single launch pad.

Also, I wonder if the traditional safety requirement of an East coast is still necessary: that's an additional constraint on location. Plus the need to be closeish to the equator won't change.

The UK is looking at West Coast locations for a new Spaceport.

Even if reusable rockets have them beat cost wise. This could be an ideal way to get passengers to orbit and back with less G forces.