I can only recommend Eric Berger's excellent book "Liftoff" to gain insights into SpaceX' way of working to get the Falcon 1 rocket off the ground and eventually into orbit. I cannot imagine Blue Origin having operated in a similar way at any point in their history.

Another problem when multiple independent orgs pool resources and work together is you either end up with design-by-committee (which leads to overengineering and extra expense, both of which are anti-goals for SpaceX and BO), or deadlock when the parties can't agree. And you'd better believe personalities like Musk and Bezos would clash a lot if they ever did a joint venture on something.

If they clash a lot it's proof they're not good at cooperating.

So maybe the answer is that Musk and Bezos are good at competing, but not good at cooperating.

That doesn't mean that cooperation is a losing strategy, but just that one has to be good at cooperating in order to succeed at it.

I mean what if all the space companies decided to use one company's rocket engine and they failed to delivery...