Using a simple back of the envelope calculation on energy requirements can tell you why. A 500km orbital altitude requires about 7.66 km/s of velocity. That's 29,337 kJ of kinetic energy per kilogram, and only 4,905 kJ per kilogram of potential energy. You don't perform an air-launch to for the potential energy savings: you do it for the reduced air-loads and energy loss due to drag from beginning your trajectory in a thinner atmosphere. This trade-off is almost never worth the added engineering complexity, as seen by vertical launch completely dominating the launch space compared to air-launch.

As for a balloon launch, well, balloons have absolutely dismal maximum payloads, so there's no way you're going to be able to hoist a vehicle with enough propellant to reach upwards of 7 km/s underneath a balloon.

Excuse me but I really appreciate your replies, so my reading of what your saying is the launch is less about reaching a height but instead reaching a velocity that can escape earth’s gravity and launching from a higher altitude just decreases the distance the rocket has time to reach this speed?

Things in orbit like satellites and the moon have not escaped earth's gravity at all. There's lots of gravity in orbit. Being in orbit is when the centripetal force from an object's tangential velocity matches the force of gravity. In other words, get thrown so fast that the arc of your trajectory continually misses the Earth as the surface curves away from you.

The only reason why you need to go up at all is the pesky atmosphere works to slow you down, making it difficult to maintain such high speeds. Satellites have to be up high enough that drag becomes less of an issue. If it weren't for the atmosphere, you could achieve orbit 10 feet off the ground if you moved fast enough.

What about vertical launch from 10k feet up, or even higher on a mountain or something, would that provide a better energy savings?

That savings has to be worth the building of expensive infrastructure at altitude, which is unlikely to happen. Air density at 10k feet yields is only 25% less than sea-level, so you're not going to see substantial performance gains. It's much better to focus efforts on choosing a launch location as close to the equator as possible where you can shoot due East (to take advantage of Earth's rotation) without flying over-top of people. This will yield much greater energy savings. There's a good reason why the world's launch locations are where they are.

you get more savings being near the equator than being high. if you can manage both you get a very small win that might not be worth it if you are far from infrastructure. better to add a little more fuel than make the satellite get shipped to your remote equatorial mountain

Almost all the energy/velocity needed for orbiting is "sideways" to the earth. Imagine needed to throw a baseball fast enough that it goes fast enough that the barely visible curve of earth falling away the same as the dropping of the baseball from gravity.

The ISS moves around the Earth at approximatle 28,800 kilometers per hour (17,900 mph).

For comparison, a bullet fired in a vacuum at only 2,000 kilometers per hour will reach about 15km up, or a reasonable ballon launch height.

I have started phrasing Earth's orbital velocity as "Mach 25" to give people a sense of scale.

For some reference, "hypersonic" is defined as "greater than Mach 5", and Google says the fastest rifle muzzle velocity is under Mach 4.

Yeah, hypersonic has really gotten the buzzword treatment these last few years.

Just to be clear, space vehicles are not "hypersonic". They travel these speeds outside of substantial atmosphere, where the speed of sound is undefined. Mach number is relative to local air conditions, ergo their Mach number isn't 25. It's undefined. Mach Number is a meaningless quantity. It's not accurate to say that a space vehicle travels Mach 25, only that it's speed is 25 times higher than the speed of sound at sea-level conditions. Saying this can be a useful reference to give context to the insane speed of orbital vehicles (as was done by the commenter above you).

I say all this to give context about the surge in hypersonic research in recent years as being something distinctly different than achievements made in space-vehicles. It's not really accurate to say it's been given the "buzzword" treatment simply because things in space already move so fast. There's a distinct advantage (particularly for military objectives) to flying above Mach 5 in the atmosphere.

There's actually a small Spanish company, Zero 2 Infinity, pursuing that seriously for small satellite launch and I was sort of surprised not to see them mentioned in the article. As other replies mention, you don't save much in terms of overall energy by launching form higher up. However, there are three big pluses to launching from high up in the atmosphere.

First, rocket engines are more efficient when they run in a vacuum than when they run at sea level. With SpaceX's Merlin rockets one running at sea level has an ISP of 282 but a vacuum optimized Merlin running in space has an ISP of 348 giving it almost a quarter more impulse for the same fuel expenditure.

Second, you don't waste fuel fighting drag as you work your way up through the atmosphere. That can easily be 100s of m/s of delta-v wasted.

Finally, launching higher up means saving weight on the rocket structures. You can make your rocket more nearly spherical and save weight on tank area. You can use a lighter tank structure since air resistance forces aren't an issue. And you can light your stages in parallel rather than series because they don't have to be stacked on top of each other or be optimized for different pressures.

https://www.zero2infinity.space/

This is a concept known as a rockoon[0]. Unfortunately high altitude balloons become really big really quickly, and even if you were starting at orbital altitude you would still need a decent sized rocket to reach orbital velocity.

[0] https://en.wikipedia.org/wiki/Rockoon

It's a fair point! It's very challenging for many of the reasons already pointed out. I'll just add that a couple organizations have actually tried but haven't yet had success doing so: https://spacenews.com/small-launch-startup-leo-aerospace-sus...