Someone on Reddit helpfully noticed that they've already kicked around this idea: https://magic.wizards.com/en/articles/archive/latest-developments/mulligans-2015-08-07
What we didn't like: This mulligan was way too strong in Constructed, and encouraged big changes in deck building. Perhaps the most notable thing was in Modern and Eternal formats, where sideboard hate got a lot stronger since you could shuffle extra copies back into your decks. Similarly, combo decks got a huge advantage since they could mulligan away possibly useless cards. In one of our biggest rules violations for changing the mulligan rule, it clearly changed the parameters for deck building, and would have a profound impact on how older formats played out.