In my experience, many pool's email notifications don't always work properly, can have a long delay, and are not necessarily relevant if your miners have just switched pools because of a problem with the pool or connection.
Using pool notifications can also lead to a lot of unnecessary emails. Say your connection to your main pool has problems, so your rigs switch pools. You get a bunch of emails from your main pools saying miners are down. After a 20 mins your main pool connection is restored and your miners switch back. Now you get a bunch of emails from your backup pools. All of these emails are unnecessary because your rigs are working fine and there isn't really a problem.
The only time I can see an advantage of a pool notification over this setup is when your internet completely goes out. The pool can notify you, whereas this setup would not be able to. Usually when my internet is down, there is nothing I can do about it, though.