Why do we have "anxiousness", but not "frightenness"?

Solution 1:

Derivational suffixes like -ness can be added to only one part of speech. In your example "anxiousness", -ness was added to "anxious", and "anxious" is an adjective. So, you'd expect to able to add -ness to other adjectives, but not to other things. This is why *"frightness" doesn't work -- "fright" is a different part of speech. It's a noun. (And *"frightenness" would be formed by adding -ness to a verb -- also bad.)

But "frightenedness" conforms to the rule, since "frightened" is an adjective. However, it's a little awkward, since it has so many suffixes, fright-en-ed-ness, and since "fright" was already a noun, it's roundabout to add 3 suffixes to get it to be a noun.

Solution 2:

We already have the noun fright and it would tend to block the formation of an abstract noun formed from the past participle: *frightenedness.