As a manager-of-managers, when I hear that a manager is doing "a lot of sitting around, waiting for stuff to happen", it's usually a sign that something has gone wrong.
Don't get me wrong: I don't expect everyone to be productive 100% of the day, but if managers are reaching a point where even they feel like they have too much free time then one of two things has happened:
1) The company has grossly over-hired for the workload at hand. If all the tasks are done and the manager couldn't find anything to do if they tried, it's possible that the company just hired way too many people or greatly under-shot their workloads.
This really does happen at some companies that get so big and profitable that executives start chasing headcount and having the biggest department they can get away with. You end up with so many managers that most of them spend their days sitting around or, even worse, inventing new and unnecessary work for their teams just to fill time. It's not good.
2) Or: Managers have too narrow of a view of what their job is. Speaking generally (not accusing the parent comment) - This often happens when developers who haven't experienced good management or managerial mentoring get promoted into their own management positions and assume their job is literally just to delegate to the engineers and then check on them until it's done. In non-stagnant tech companies, there is always more for managers to be doing: Reviewing/updating documentation, helping with hands-on testing of the product, observing or interacting with customers to get a deeper understanding of the problem, coordinating with the sales team to get a better understanding of their domain, and the list goes on. Many of these tasks aren't immediately obvious without proper managerial mentorship, and they might be downright foreign if your only experience with managers has been of the delegate-and-wait variety.
Personally, my experience was that I was far busier as a manager than I ever was as an IC. IC work is more narrowly scoped and easier to constrain to specific time limits, or get targets and deadlines shifted according to however much work could be done. As a manager, the amount of work that could be done was both never-ending and also extremely varied, comprising tens or maybe hundreds of possible tasks that often needed attention in parallel, combined with the inter-personal demands of managing people and constant hiring.