Why no double “v” in “river” or “quiver”

"vv" used to be considered equivalent to "w"

For one thing, double VV/vv was previously used to represent a different sound: /w/. Nowadays we always use the form w, originally a ligature of vv, but during the era of early printed material, we have clear evidence of VV/vv being used equivalently to W/w (discussion and examples can be found in "Transcription of Early Letter Forms in Rare Materials Cataloging", by Deborah J. Leslie and Benjamin Griffin, 2003, pages 4-7: "III. I/J, U/V, and VV/W").

I'd guess that this use of vv inhibited the development of "vv" as a spelling of the /v/ sound after a "short vowel". Current spellings with the sequence "vv" are all relatively new, and I believe postdate the standardization of W's ligatured form.

Unlike other double consonant letters, "vv" never occurred as a long consonant sound in English or source languages

The use of double consonant letters in English after short vowels is a widespread pattern, but it is far from regular. There are a number of cases where the use of double consonant letters has been influenced by etymology in addition to, or instead of, the pronunciation of the preceding vowel letter. And unlike other consonant letters, "v" never has etymological reasons to occur double.

Some present-day double consonant spellings correspond to originally long consonants in Old English. But the consonant /v/ was never originally long in English, because in Old English, [v] occurred only as a short consonant (usually spelled f and considered by modern linguists to be a contextually conditioned pronunciation, or allophone, of the sound /f/). This is because Old English [v] developed from short /b/ or short /f/ in certain conditions, but long /bb/ and /ff/ remained unchanged in the same conditions.

Some present-day double consonant spellings correspond to originally long consonants in Latin, since Latin long consonant sounds were spelled with double consonant letters. But Latin doesn't have words with a long consonant "vv".

There are certainly many English words spelled with a double consonant letter for non-etymological reasons (such as grass and brass from Old English græs and bræs or hull from Old English hulu). However, although these particular words were not spelled with double consonant letters in Old English, the double consonant letters ss and ll did exist previously as part of the Old English spelling system as a whole ("ss" is etymological and goes back to Old English in kiss, "ll" is etymological and goes back to Old English in hill.) The non-etymological use of double consonant letters that becomes common in Middle English likely developed by analogical extension from the spelling of words that originally had long consonant sounds. The lack of etymological basis in any word for double -v- could be a contributing factor to why -vv- only arose slowly as a doubled spelling of the consonant /v/.