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There is nothing that is necessarily slow with capability-based access control. I think you might be confusing it with slow message-passing in classic microkernels, for which capabilities are sometimes used for referring to the message ports. But that is just one way in which capabilities can be used, and it is not the use of capabilities that makes them slow.
Capabilities is first and foremost a way to model access control as primitives.
WASI got its model from CloudABI’s libc, which is a libc restricted to use only Capsicum capabilities. Capsicum is part of FreeBSD UNIX (implemented in its monolithic kernel) and have been used by several of its standard utilities for years, with a negligible performance impact compared to earlier.