Given the Swift goal to promote clarity over brevity, I would prefer having to explicitly mark existentials (at least for protocols having 'Self' or associated type requirements, PATs) with any Protocol instead of simply using Protocol.
Whenever a PAT is placed as an existential, the compiler would let the user choose which fix-it to apply: either using a generic or explicitly marking the protocol as existential with any.
The benefits of having explicit existentials are available in the Clarifiying existential types section of Improving the UI of generics.