In many schools, children are identified as “behind” with reading
before they would even have started school in many other countries.
Despite how it looks, this is not:
- would + [have started] == would + [present perfect]
This is in fact
- would have + [started] == would have + [past participle]!
which yes, I know is immensely confusing, but when you look at it as "would have" + past participle you'll see that it falls into the "third conditional".
We use the third conditional (if + past perfect, would + have + past participle) to talk about something in the past that did not happen.
And I would say that this is exactly the appropriate tense because it describes an event in the past that did not happen at all.