Earlier quoted context omitted.
Then you joined big tech at the peak of the pandemic boom, when it was completely fair game to for recruiters to be poaching even foreigners due to the outsized growth outlooks. You should be aware that the economic environment has basically taken a 180 since then, and your experience might be very different from someone joining the workforce today with no work experience. To counter the "cram LC" thing, the issue is…
Is my impression wrong that the major tech companies will give anyone a chance to do the initial online assessment with a pulse?
One is that sourcing recruiters are not equipped to handle technical screening logistics. They can't tell, for example, if a solution works but has O(n^2) complexity, or if the candidate failed because the tool was being stupid in some way or the question was phrased ambiguously.
Another is that OAs can be gamed much more easily than face-to-face phone screen sessions (see, for example, reports of indian "study" groups).
Another issue is that the evaluation criteria for OAs is often so coarse that it does not provide a reasonable level of filtering, compared to having a combo of a good sourcing team + an engineer "guarding the gate" so to speak via the phone screen session. An engineer's technical screening skill is considered non-automatable enough that companies would fly them into school fairs to vet internship candidates.
Teams may not even trust OAs that they didn't devise themselves, nor have the actual inclination to develop/maintain their own OAs.
OAs also tend to gravitate towards trivia-style quizzes that are often associated w/ "lesser" companies.
There may also be concerns about being respectful of candidates' time.