To be done after 1.15-stable is branched.

Scan the codebase for deprecations marked with a 1.16 deadline and remove them (ack deprecation.*1.16). All deprecations with a 1.16 deadline have been shipped (at least) in 1.14 and 1.15.

Marked for a 1.15.0 release so it's done at the time of 1.15-stable branching, but please move to 1.16.0 when done.