Was thinking about this in mathematical terms recently, in terms of what's
efficient vs. what can
scale. In general, managers can't do things for reports that don't scale fairly across their whole team, because otherwise it'll give the appearance of favoritism for those reports who get favors and demotivate the rest. So to a first approximation, a manager with N reports can devote at most 1/N of their time to making a report's job easier. (To a second approximation, it's more like 1/2N because the manager also has overhead tasks like 1:1s and performance reviews that scale with the number of reports. To a third approximation the denominator scales supra-linearly after about 10 reports because you start taking up all your time with management tasks and have literally zero time for project work.)
Their goal is to keep their report's time fully utilized, so it is logical for a manager to take on a task if it saves their report 2N as much time in IC work. For example, a manager with 4 reports can devote up to 10 hours/week fairly to each one; taking the second approximation, that's 5 hours of overhead and 5 hours of project work. The report has 40 hours/week of time. Therefore, it makes sense for the manager to do a one-hour task (say, design work) if it saves the report at least 8 hours of work. A manager with 10 reports can devote only 4 hours/week to each, so with 2 hours of overhead and 2 hours of project work, it makes sense to take on a one-hour task only if it saves the report 20 hours of work. Taking the third approximation and assuming overhead is a constant 2 hours/week/report, the first case becomes 8 hours of project work, and so a task makes sense if it saves the report 5 hours of work.
You can see how a manager very rapidly approaches the "Do nothing other than bare minimum performance reviews, 1:1s, and save the report from blatant stupidity" line as their reporting load increases. This is why so much moderate stupidity and waste persists in big companies: the manager is not incentivized to remove it (and doesn't have time to anyway), but the report does not have the organizational power to change it. And ironically flatter hierarchies tend to be worse at this, unless they have ICs step up and do the "improve efficiency for everyone" role, but then they're usually either promoted into management or they leave.
This is also why managers look chronically dumb and entitled to ICs. The IC can see plenty of opportunities where "If you just did X, which takes 15 minutes of your time, it would save me 2 hours of my time." They don't realize that their manager has 10 other reports, so a.) their manager does not have 15 minutes of time to spare and b.) their manager is only going to spend it if saves at least a day. Otherwise it makes more sense for the employee to do it themselves, simply from a scalability perspective.