As the other commenter already pointed out, it's the mass that's the limiting factor here, not the cost. The key idea here is that rockets and jets need two things - a reaction mass and energy. Scramjets and other air breathing engines don't just take oxygen from the atmosphere. They derive much of the reaction mass also from it. Even the inert nitrogen absorbs heat from combustion and acts as reaction mass. The primary purpose of the fuel onboard is to provide the energy. It's contribution as reaction mass is only secondary (note that this is for air breathing engines). This is very evident in the case of turbofan engines, where much of the thrust is contributed by the uncombusted air from the fan.

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.

LOX halfway to orbit is significantly more expensive than the same LOX delivered to the launchpad.

Its not the cost, its the mass you're trying to reduce. So far, the engineering challenges have made it unfeasible, but its not a surprise that people look at the hundred tons of LOX on a rocket and imagine exchanging it for payload (or aircraft style re-usability).