Here's what I found: Stencyl doesn't run iOS simulator directly - it uses a utility called ios-sim. ios-sim accepts a command line argument, --stdout, to redirect stdout to a file. The file being redirected to by the lime/openfl/Stencyl dynamic trio is under /private/var/folders/ etc. etc. It's a long path, and if I remove the log file manually and run the simulator through Stencyl, it doesn't create a new one.
If I specify a log file under my home directory (by running ios-sim directly from the command line) I do get a log. So this seems to be a permissions problem, but I can't figure that out, since the directory ios-sim tries to write to is owned by my user, and I don't have any problems writing to it from the command line.
In any case, it looks like whatever Stencyl is doing in its current configuration isn't working.