You can view the fonts. You just have to dig a little deeper. Tap on the sub-font descriptions; Light, Medium, Regular, Whatever. This displays a font sample.
Unfortunately this only works with the "More" fonts after you download them. But you can remove the unwanted ones under My Fonts.
I've never done much with the Fonts Settings. The current settings are new to me, so I was rather surprised at some of the things there. Also, I'm running the public beta, so it might be different there too.
At least one bug is that the search bar in the photos fonts selector does not work. I suspect what we are seeing is a bunch of code that is meant to be common to many apps, but who's features are not yet a part of all the apps. Similar to the way you can paste a picture into another picture. There is no way it works that way by design. It's just too awkward.