Actually I can’t win here 
Listing tags alphabetically changes order at /tags too.
When I’m tagging topics context is important and we westies read from left to right and we see list of tags as a sentence with some meaning.
But /tags is a directory and there we expect alphabetical order, because popularity in long directories is too abctract and tells what everyone else has done, not what an user is looking for — again, the context is missing.
I don’t expect that the team start code drag&drop system or ”using order”, because benefits aren’t in balance with workload. So, I live with that and because UX of /tags is way more important than theoretically aspects of how tags are listed in topics I keep listing tags alphabetically instead of popularity.
Well, I’ve learned some new things today. Minor ones, but new. So, time is not wasted