味わわせる often pronounced as
味あわせる? What makes the former form unnatural, and what is the mechanism that changes it to the latter form? In the first place, what it the
-waw- attached to
aji (besides the obvious answer that it is an affix that derives a verb)? Are there other words (inside or outside of Japanese) that follow the same phonological pattern?
I can only speculate that this is a kind of onbin to ease pronunciation. The two medial approximates /w/ are only separated by a vowel. Approximates, also known as semi-vowels, share some similarities with vowels. The reduction of one in rapid speech is small while still understandable. The reduction of the first rather than the second is similar to baai <> bawai, which tries to avoid repeating the same vowel twice.
I would not say that the former is necessarily unnatural. Rather that in spoken language the former takes more effort to say and as such sounds stiff or formal. See above for speculation for the mechanism.
As you already said, it is just an affix that attaches to nouns to derive verbs. Etymologically it is suggested to be 這う・延う, but evidence is minimal. There are both yodan and shimo nidan versions.
If you are asking for other words with the same affix waw-, then yes.
And then there is the nominal forms (cf ajiwai), though the corresponding verbal forms do not seem to exist:
These are more verbal than affix, but for reference, there is also: