Paul Banks notes that we aren't very clear about what Push is good for. Something like this is probably a good idea:
The Push API is intended for infrequent messages. If you have a page
open to site, it might still be suitable to rely on push for messages
that are infrequent or unpredictable. However, if you are actively
communicating with your site, it is best to use more direct means of
sending messages, such as HTTPS.
Paul Banks notes that we aren't very clear about what Push is good for. Something like this is probably a good idea: