I don't think they are worth the investment, but I suppose opinions may vary on that. It depends on your situation, really.
On very hard, you don't have to DoW after you kick off the BB wars, excepting a very few countries. So, stability won't be a problem. Any stabhits taking you below 0 will quickly be corrected by DoWs from AIs.
On hard or below, though, to conquer the world (if that is your goal), you do need a lot of stability investment, because after a point most or all of the DoWs must be yours. And as you get big, incorporating lots of wrong-religion provinces, your stability cost will be very high. Also, once you are "over the hump" in a world conquest, you don't really need tech any more. You'll have plenty of income. In this situation, FAAs are probably the best thing you can build. This is probably the situation that Ericus1 up there was thinking of.
For any sort of game where you don't conquer the world, you can select which provinces to take, and should generally not have many wrong-religion ones. You may have pagans or wrong-religion same-culture provinces for a while, but you'll convert them. In this sort of game, income (and tech) matter, and you'll want to be buying breweries.