What is the point of saving mass here? LOX is cheap, so it isn't the cost of the LOX. Does saving LOX make the vehicle cheaper? No... it increases the quantity of fuel needed, which (particularly if it's LH2) makes the empty vehicle much larger and more massive. This is doubly bad, since every last gram of that empty mass is taken to orbit, unlike the mass of LOX.

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.