There's also cases where we have students spend a long time on truly useless stuff because none of the teachers involved understand that it's essentially useless. The example I'm seeing with my kids right now is "mixed fractions". They bang on and on about them... but they're just a special case that is basically used by cookbooks, and not much else. You don't need to know what 37 8/17s + 98 3/24s is, because the only mixed fractions you're likely to see are ones you'd see in recipes. 3½ is pretty large as mixed fractions come in the real world. I don't think I've ever seen in my entire life a mixed fraction as large as 12 4/5. They're always written some other way; 64/5, 12 + 4/5, 12.8, but never a mixed fraction.

In high school, I remember spending endless hours on trig identities. They are useful only in a similarly small situation. (And I actually think they're a fun target to fire Taylor polynomial expansions at, as a good exercise for using them and understanding infinite series, but even then, rather than "memorize this pile of identities" it becomes "prove or disprove this statement:", which is different.) There's a dozen things that time could be better spent on, by purely pragmatic or purely academic standards. But nobody responsible for the curriculum realizes this.

I also recall some really abortive graph theory introductions and set theory... I'm not even sure I see the value in the terrible "15 minutes in high school" types of introductions of those topics. Nobody comes away with anything of either (again) academic or practical value, despite the huge value of the topics themselves.