I've only gotten up to doing an MSc (currently volunteering for Vikash Masinghka in my Copious Free Time), but I do know a hell of a lot of academics.

From my (second-hand) knowledge, easy quals are an artifact of something very like economic privilege: your school is very prestigious and doesn't need to cull its grad-student herds as much as others, so quals are allowed to be easy. In other places, quals are used to evict many grad-students from their PhD program because resources are more scarce.

but it seemed like MIT grad students also often started doing research fairly early on, from my perspective as an undergrad there.

I don't know anywhere where grad-students don't start doing research as early as possible. Do some programs really involve whole years of just classes?