Your communication channel between Alice and Bob is, itself, a capability (or a collection of capabilitys) that grants Bob memory write, Alice memory read, but does not grant the ability to transmit a capability from Bob to Alice.

Absent a misunderstanding on your part, the only way I can coherently interpret your argument is that you are arguing that the presence of kernel data structures mediating the handles somehow makes it not a capability system. That there is some background element mediating the validity of your capability representation and thus that is just a MAC layer; unless you can write the byte representation of your handle into memory and somebody else can read it out and then have access to that resource it is not a capability.

One, that allows forging capabilitys unless they are cryptographically secure against collisions.

Two, the actual essence of capabilitys is not being bearer tokens, it is non-construction. Capabilitys are derived from existing capabilitys, not manifested into existence. They have provenance. It is the OS equivalent of not allowing programs to cast arbitrary integers to pointers and thus manifesting pointers into existence which breaks basically every high level memory safety guarantee. You do not allow programs to cast arbitrary data into handles to resources which is what ambient authority systems effectively require.