[jkqwzsoo]

This is "saying the quiet part out loud" in academia. For engineering undergrad, your in-state university (ABET accredited) will usually be your best cost/benefit option (unless you're going to MIT, Stanford, or, for CS only, CMU). For grad school, I believe you'd want to think very carefully about the opportunity cost (and what you want your PhD for) before going anywhere outside of the top 20 (or even top 15) schools in your program. For a postdoc, where your opportunity cost is even higher, I think you need to be in the top 10 (or top 5) for it to be worth it.

There's no reason to do a postdoc at any school outside of the top 10 in your field unless, as you point out, you're working for an exceptionally well-regarded PI who is particularly going to be able to move your career in your desired path.

The people who do postdocs at these institutions are usually foreign, for whom a US postdoc is gold. Come to think of it, I can't recall ever interacting with a university postdoc who was a US citizen -- I've only worked for one "PI-generating PI", who happens to not like hiring postdocs.

[throwawayarnty]

Academia beyond postdoc is so competitive that even being in top 5 school is not enough information to decide whether it is a good idea.

Even within Harvard, the percentage of postdocs getting faculty positions is low.

One needs to calculate essentially how likely you will get a top publication in that lab.

The arithmetic is something like for a research group, what is the average number of top publications per year per postdoc. Many top labs at Harvard don’t do well with this metric because they have like 20 postdocs and 1 top paper a year.

Another metric is what fraction of postdocs end up in good faculty jobs.

[bertday]

Postdocs are sometimes used as a mechanism to play games with tenure rather than getting the an academic job. You get a publication “head start” without invoking the countdown, and you already often have a future job in hand early.