ARAM repetition - not very random?

(Note: This is subjective. YMMV.) I'm consistently (re-)rolling champions that I've recently played in ARAM; despite having 66 unlocked and the weekly free rotation to choose from, it doesn't seem very random.

Can we consider almost-randomness where, if necessary, one spends an extra few seconds in the queue in order to be far less likely to roll a duplicate champ from the last N matches (where N is some metric possibly based on # champs unlocked)?

Same for re-rolls -- getting a champ I had last round and then spending a re-roll that gives me the champ I had two rounds ago is a bothersome waste of something I earned.

Further, a player with fewer champs is more likely to (re-)roll duplicates, so this suggestion could possibly work across the board for all ARAM players...

EDIT: About the poll -- let's assume "all things being equal" for the suggestion (as in, it wouldn't greatly expand queue times, etc.) Voting yes or no because it may or may not break something or be easy/difficult to add (we are not qualified to judge either) is not the question being asked.