PS: I have seen early-stage (but successfully tested) scramjets being developed for this purpose.
We have to ask: what exactly is a scramjet vehicle delivering? It's enabling the use of air instead of liquid oxygen. But how valuable is this? LOX is the second cheapest industrial liquid after water. The fuel part of a rocket propellant combination typically dominates the propellant cost. If a scramjet launcher uses more fuel (especially hydrogen) than a rocket vehicle would, it will end up increasing propellant cost per unit payload to orbit. It will also likely increase propellant volume per unit payload to orbit, especially if LH2 is used (LH2 being just 5% of the density of LOX).
All scramjet launchers need a rocket to reach stable orbit (since a scramjet cannot produce thrust at apogee to circularize above the atmosphere. So one can ask, what the tradeoff between the delta-V this rocket provides and that of the scramjets? From what I've heard, all such trade studies end up optimizing to 100% rocket and 0% scramjet.
A scramjet stage will be very light compared to an equivalent rocket stage, since it carries only the energy source (fuel) and not the full reaction mass. If this scramjet stage is able to impart a velocity close to the orbital velocity by the time it reaches the upper atmosphere, the subsequent rocket stage will have much less work to do to get it into orbit. And that translates to much less propellants (including oxidizer) and much less mass in the upper stage. It's not necessary to collect oxygen from the atmosphere to see an advantage.
Obviously, the raising of the perigee at apogee is going to need this rocket engine again. There are no launcher concepts that depend purely on scramjets.
Minimizing fueled mass of the vehicle is a stupid thing to do. It's optimizing the wrong metric.
Scramjets also suffer from bad thrust/mass and thrust/$ ratios compared to rocket engines.
Overall scramjet launch vehicles are an example of pyrrhic engineering: even if one could make such a vehicle "work", no one would want it.
Scramjet launchers (and air breathing launchers in general) have been looked at extensively, for decades. They don't make any sense. The math just doesn't work. Here's an insightful post from the Old Usenet that illustrates the difficulty:
https://web.archive.org/web/20220131115058/http://www.island...
When reading that, remember that LOX is 20x the density of LH2 (or 17x the density of "slush hydrogen").
"Rockets, not air-breathing planes, will be tomorrow's spaceships"
(New Scientist, 2009)
https://web.archive.org/web/20101017031109/https://www.newsc...