These days, I pretty much don't install apps on my phone. I just use it as an everywhere web browser and live with the web version of various things.
You could actually do that through the Facebook.com web interface much longer than you could through the FB mobile app. Of course, you can still do it on the web, though it's a separate domain (just as, on mobile, it's a separate app.)
But since they really want you to use the Messenger mobile app, to use the web interface on mobile you have to use "Request desktop site".
My 'SLA' for facebook messages is about 24 hours, and people who send me things there learn that over time. I generally just tell them why I don't see their messages right away.
In general, I make a point of not being too responsive with any online/async notification systems, except for SMS. It's one way I keep myself from being so scattered.
Yet you still have to bring the app to the foreground, but this is potentially a huge privacy leak IMHO.
The "doodle fruit ninja run" game I play don't need to now that my girlfriend left me so they can display a tinder ad...
(Oh, god if an evil ad developer come here don't take this as a good idea)