I haven't had time to properly digest and contemplate the argument @dabrahams is making yet so nothing I say here should be considered as a direct response to that. However I do want to point out now that the statement above is simply not true.
Lifting the restriction would significantly simplify designs that store type-erase values and use various dispatching strategies to interact with the existential. The current workarounds I'm aware of rely on introducing an additional protocol which can be used as an existential and dispatching through that. Lifting the restriction would allow storage, casting and dispatching to happen directly on the PAT protocol itself which would streamline designs significantly. I have kept this pitch in mind since it began and have already run into several use cases where it would be extremely handy.
I don't have an opinion on this syntactic change yet but I don't buy the argument that it will reduce accidental use of existentials. The reason users often reach for existentials is because many programmers are most familiar with Objective-C protocols or interfaces from other object-oriented languages. The will reach for a tool that feels familiar in this way regardless of the syntax used to invoke that tool.
Allowing extensions on the existential would be a really useful way of allowing existentials to conform to protocols (including their defining protocol). On the other hand, allowing extensions on existentials could introduce significant confusion between those and protocol extensions. I think we need to study the use cases and consider alternative solutions closely before heading too far down that path.