Bayes, I don't want to get drawn in an unnecessary fistfight over this but I know several predocs at top 10 who take Real Analysis for the first time as predocs. Top 10 PhDs are far far harder to get into than predocs, partly because until recently predocs were largely restricted to domestic students (MIT SEII still might be restricted to domestic student). The inelastic supply of international students, along with their vastly superior preparation in terms of coursework (they often have taken the entire PhD core), means that domestic students are forced to exploit their comparative advantage in applied research. Often, this means less focus on math and more on actually doing RA work since early in undergrad. In fact, at my predoc, most predocs are not sufficiently well prepared to take PhD level first year courses (and in fact mostly opt to take 2nd year courses). There are a large number of incentive issues too here, because often not taking PhD micro is better than taking it and not getting an A.
See here the people taking MATH 301 are predocs taking analysis for the first time. One person is taking grad micro for credit out of 30.
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Also, yes, I don't believe it is worth it to go to schools outside a certain range as they just become a way to exploit cheap labour from grad students via teaching assistantships. You want to have fun teaching intro micro while taking a full load of grad courses just so you can get your meager 15,000 stipend go for it. But don't sell these idealistic pipe dreams to people, where they slave away for 5 years at a program only to get jobs they could have had with a bachelor's degree.
Frankly, you sound like a bitter and jealous person by insinuating than I am not a predoc; I don't have anything to prove to you or anyone else and I am just offering a pathway for people who didn't go to Ivies as undergrads to get into predoc positions. I didn't go to an Ivy or a top 15 phd granting school (I went to a top 15 LAC) and I got into a predoc just fine. If any curious person reading this really wants to verify my credentials they can do so by messaging me and I'd happily tell them who I am.