They won’t even let you view messages on the mobile website either. Instead they restrict that and force you to install the Messenger app. Yelp does the same thing and feels just as scummy of a tactic. Basically both companies try to force you to install an app you don’t actually need so they can mine your contacts and personal data. No thanks to your tricks and traps business model.
You can also tell your browser to view Facebook in desktop mode, and you can then see the messages. Not a pleasant user experience, but fine for the rare times when I need it.