I just did a system update and got configuration diffs like

-               i=$(($i + 1))
+               : $(( i += 1 ))

If you don't know : builtin yet, read first entry of "SHELL BUILTIN COMMANDS." I have been using it quite often with infinite while loop, e.g.

while :; do
  do_something
done

I never thought of putting something behind it, and that diff is quite genius in my opinion. However I will just write

(( i++ ))

I don't see there is a reason for using Arithmetic Expansion, Evaluation is enough and clear. Expansion will returns the expanded string, which cause command execution if you don't prefix with :, and you will get "command not found" error.

There is a good use of :, putting it after last command of a function or last command of a script, if they have chances to return non-zero and you do not care if that command runs into problem. This way it will clear out the returned value.