There’s still bias. Parent has to care. Transport is often an issue. And the school usually gets to reject children with any sort of disability or other negative trait.

Most of the lotteries aren't automatic entry, etc. You still need a parent to fill out the forms and stuff. Some even rely on GPA, diversity metrics, or entrance essays. There's definitely selection bias, you just encounter it prior to the lottery drawing (or other selection process).

> Charter schools are frequently oversubscribed, and admit students via lottery. This makes it pretty easy to run randomized tests that aren't affected by selection bias.

No, it does not, because the following sources of selection bias exist.

(1) Charters select for actively involved parents, because they are not the default-assigned by-residence public schools, and an active choice is necessary to get into the pool,

(2) Charters, because they are not scaled to only take the actively-choosing parents from the catchment area of a typical district school, select for parents with greater means who are able to make a longer travel to the school for drop off, pickup, and other necessary interactions.

(3) There are often biases in the lottery system; even something as simple as giving favorable consideration for having a sibling already in the school reinforces the impact of other biases.