Short answer: you still need a complex vehicle to finish the orbit insertion after getting thrown, and now you have the added complexity of designing your (smaller) rocket to a) survive a massive g-force while being thrown and b) fit into the catapult sling. So far the tradeoffs haven't been worth it.

Basically the only things we know of that can survive our spin launch systems is stuff like 'very crushable food supplies' or 'a giant lump of steel'.

So you save a bit of fuel but you need to invest 10-100s of millions into a ground infrastructure. And then you are limited to one launch site and limited in orbits you can reach.

Then you still need to design a rocket. You still need a rocket engine and all the other parts of the rocket. So even best case, you only eliminate like 60% of the cost. Now you have to completely different engineering teams with little overlap in skills.

You can only build tiny rockets. In order for your accelerator not to be just completely absurd in size and cost, your gone build a rocket in the 100-200kg range. For that you can maybe ask for like 5 million $. But SpaceX is already doing that at far lower cost. And you don't even have the same flexibility of costume orbital insertions as other small launchers do.

Small launchers are a bad business, of the 100s of small launch companies, the only one that has had any success is RocketLab, other then them its a graveyard.

It will be hard to impossible for your rocket to be reusable. So you need to build the rocket for sub-1million $ including the launch to compete.

But then ... you need specifically designed sats that can handle the acceleration. So you need costumers to specifically design their sats to a complete different standard then for your competitors. And why would any costumers do this if you significantly cheaper then your competitor. Spinlaunch has started to develop its own rocket components that they hope to get other people to use.

But there are many other potentially things on a sat that could break, so for most costumers its simply not an option.

The industry has been moving to larger sats, the old idea of cubesats has gone and even small sats are regularly 200kg or more. So the market for anything below is pretty tiny, and the market for sats of less then 200kg that can handle 10000g is even smaller. And the market for 200kg sats that can handle 10000g and want to go into the specific orbit that you built your catapult for, is even smaller.

If there were many 100s of launches available, just desperately looking a way to get sats to a specific orbit, it might be worth a discussion. But there just isn't.

This kind of technology might make sense on the moon, if you want to bulk export something like ice.

There are companies in that space.

https://www.spinlaunch.com/