I'm worried about the strategic implications of this. In the single-winner case this is Majority Approval Voting (assuming you're using the Droop quota), and even with more winners this has all of those strategic issues.
- Suppose you are part of a faction that comprises ~1.2 quotas and has fielded two candidates, one of whom you like more than the other (you hate every candidate outside of your faction). Your faction is very likely to win one seat, but it won't win two. Here you want to have your ballot count only as an approval for your favorite as far into the tabulation as possible, so you shouldn't give your second choice a score greater than 1. Even bullet voting is reasonable; if the vast majority of voters in your faction are giving their second choice a 1, bullet voting is the only way to make your ballot count in the decisive round. (This is, of course, the chicken dilemma.)
- Suppose there's a two-party system. The other party has both moderates you tolerate and extremists you hate, and you'd rather they elect more moderates than extremists. Still, the main thing you want is for your party to win more seats than them. Here, giving even a 1 to a moderate candidate in the opposing party is a big mistake. It won't make a difference at all until all scores of 1+ are counted as approvals, and at that point you still want to favor your party's candidate over the opposing moderates.
These are simplified examples, but the simplicity is not necessary for such problems to manifest. I'm not claiming that it's never strategically optimal to give a candidate a 4, but it's pretty atypical. It's strategically optimal to use lower scores than other voters do, such that they're supporting both their own favorite(s) and your favorite(s) while you're only supporting your favorite(s). The only equilibrium involves 5s for a voter's favorite(s) and low scores for everyone else.
Under Threshold MES, voters who ignore strategy lose a lot of influence, and when voters are strategic the expressive power of the 5-star ballot is mostly wasted. I am pessimistic about it reducing political polarization any more than any other PR method would; I actually expect it to be worse than STV in this regard since parties would be heavily incentivized to get their voters to not give candidates from any other party a score greater than 0 and this would encourage divisive attacks. Similarly, candidates would be incentivized to play exclusively to a party's base (and perhaps to some "sucker" voters in other parties who vote as would make sense in single-winner STAR).