Lots of very good ideas in this thread.
I'd benefit from Ableton adding tap-tempo buttons to the Live effects that can be synced to a tempo or repeat; like the delay effects for example.
Using this tap-tempo would only set the rate of the effect being tapped, & have nothing to do with the global tempo, or effect an Arrangement in any way.
This could be an option other than having the effect sync to the global tempo or master clip tempo.