Here is Megan on that topic, I agree with much or maybe all of what she says, namely that parents are seeking quality peers for their kids rather than school effectiveness per se. But I’d like to add another, neglected factor.
If you look at the benefits of opening up international trade, it’s now well-known that the decrease in deadweight loss may be fairly small, but the gains from “putting under” inefficient firms can be large. You are winning rectangles instead of small triangles, and in the longer run innovation spreads more widely and prices can fall with higher overall productivity levels.
OK, so now consider schools. Vouchers typically are applied to pre-existing schools, and often in a fairly limited geographic area, such as a single city. Those schools already had a stable place in the market, and now the demand for their product goes up. The experiments typically are designed so that no public school goes under.
So, post-vouchers, no schools go under, including no low productivity schools. Thus the efficiency gains from vouchers of this kind can be quite small, possibly zero.
Of course you can debate whether we should ever let K-12 schools fail, or under what terms. But the general principle remains that markets are most potent when exit is an available and indeed exercised option.