Facebook – Disable ‘Turn on Notifications’ Popup

It looks like Facebook has done another update so everyone gets more notifications. This thread on the Facebook forum has a couple of solutions suggested, this one seems to have the most love:

Go to the top of your screen and click the little globe symobol where you can view your recent notifications. Hover over one of the them on the top left and click the X. It'll ask if you want to turn off "top friend" activity notifications. Click yes. They will still appear in your news feed, you just won't get notifications for it all.

On a side note I think the icons you've circled in the first picture have more to do with identifying the notification than close friends (photos & status get the star, links get the pin).

Updated

Click the Notifications globe at the top of the Facebook window and when the drop-down drops click the Settings link (the little X's next to each notification have been removed recently). In the "What You Get Notified About" section, you can edit and turn off "Close Friends activity"

Unfortunately, there is currently no way to do what you're asking to do, and likely will not be. Facebook's customization options are deceptively sparse, and they intentionally limit user usability in order to maintain more direct control over the content users are exposed to. There is a surprising lack of other obvious features, in (for example) Newsfeed options, like the option to only show posts made by friends, not displaying as major items posts that they like or are merely tagged in.

Mack nordstrum mentioned the settings at "https://www.facebook.com/settings?tab=blocking". This will solve a few of the problems you mentioned, but requires you to individually specify either specific friends whom you want to block ALL app invites from, or select the individual apps themselves to block or unblock. An option to block all from the get-go, regardless of user, before you ever get your first invite at all, is unlikely to be made available because it conflicts so strongly with Facebook's business model. To answer your question of why the burden is on you, the user, to swat these pesky apps one-by-one: You, the user, are not the one paying facebook money. The creators of those apps are.