macOS 10.12: Audio always stuttering and skipping on MacBookAir6,2

On the 2013 MacBook Air 13" with macOS 10.12 Sierra, my sent and received audio with the default settings sounds as if it is losing many packets. The info window still reports 0% lost or late packets, even when people talk for whole minutes, so I don't think it's a network problem, and could be related to some internal changes in macOS. This issue is not present in OS X 10.9.5 Mavericks, which I installed as a test, and all audio works as expected with no problems in 10.9.5. I could not find any settings in Mumble 1.2.17 or macOS able to solve this issue.

I thought this was another Broadcom WLAN issue, but it appears not to be. Card is AirPort extreme (0x14E4, 0x117) with a BCM43xx chip (System Profiler doesn't say which in particular.) I'm connected over 5Ghz Wireless-n and have a 90Mbit broadband connection. Switching to 2.4Ghz mode makes no difference.