Having 17 direct reports is too much. Managers are not just a link in the chain of command. They also do stuff that needs to be taken care of. All kinds of unusal things happen and not all are suitable for delegation. 17 direct reports is not only a measure of how many colleagues they need to manage. It is also a measure of the large the weird-things-that-needs-taking-of-scope is.
Seriously. The most effective teams I've ever worked in, had 3-5 people under a manager. The manager occasionally got their hands dirty when they could spare the time, but in general, "getting every roadblock out of 5 people's way" is a lot of work, and combined with all the non-delegatable stuff, would keep them pretty busy.
When a team grows much beyond that, the manager is no longer removing all the roadblocks. They're doing all that other stuff that _can't_ be delegated, and the team under them is now spending time doing stuff that _technically can be delegated_ but would be much more efficient for the manager to do.
Typically what happens then, is one of the underlings becomes the de-facto also-manager, relieving the burden from the rest of the team and increasing overall productivity by re-centralizing certain duties. However, this hurts their individual productivity metrics, so in bean-counter companies this is a hazardous move. It's safer to not help the team and just let the sick structure shamble on.
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.
The biggest one I've encountered is just scouting out problems before handing them off to an IC, to ensure they're framed correctly and the IC will be able to make rapid progress on them.
Some of the levers a manager can pull to make the IC's job easier are: 1) negotiating with PM/UX to accept a solution that might have 80% of the user benefit but is 10x easier to implement 2) lining up commitments from partner teams before committing their own resources 3) lining up schedules so that all the people on a project are working on it at the same time, regardless of which team they're from 4) arranging to colocate people from different teams who will be working on the same project, to cut communication overhead 5) doing #1 to change the architecture and eliminate the need for partner teams altogether, avoiding #2-4 and cutting communication overhead 6) pointing the report at a potential solution early so they waste less time hunting around 7) answering simple questions from other teams so that it doesn't take your own engineers out of flow 8) buying off-the-shelf solutions when appropriate to scale down the project 9) killing infeasible projects before they get to the engineers.
All of these require time and technical knowledge, though. An engineering manager with 16 directs is unlikely to have time to do anything other than performance reviews, meetings, and reassigning work that comes down from product/UX/sales. A tech-lead manager with 4 directs can devote some of their time to architecture & design, which then feeds back into resourcing and project assignments.
The goal of a manager ought to be to maximize the effectiveness of a team, which does not directly mean fully utilizing time, especially in a software development context.
Often some slack in a team results in the team as a whole being more effective.
Your final paragraph is why it's so important for companies to grant formal titles to their ass. managers. You can effective manage a large number of direct reports, if you have an assistant to handle the other half of your job.
