In Modern English Usage if I recall rightly Fowler gave detailed list of words where the -en conversive suffix is necessary, allowable, and unwanted.

Some adjectives have to take it to become verbs. You can't hard or soft or dark something: you harden, soften, and darken it.

At the other end, you wet or smooth something: the verbs wetten and smoothen might exist, but the only excuse for using them is if you desperately need the extra syllable in poetry.

To me, quieten is the normal word and I would have said there's no verb "to quiet". Well, I suppose there is, but I would never say I was going to quiet a baby or a crowd. However, it seems from the above that it's acceptable in N.Am. usage.

In between are words where both occur: to damp or dampen something. I think I'd damp abstract things like ardours and dampen things like towels.

The first seems to be the largest category: blacken, sharpen, steepen, moisten, redden, freshen, etc. etc.

The suffix only goes on old monosyllables so there's very little room for neologism, but I recently used the word "pinken" feeling I was inventing it; then promptly met it twice in Amy Bloom's Love Invents Us (plug for wonderful novel).