I don't believe a manager can be effective at 15 direct reports. I think it's possible to keep things afloat, but split that team in half and hire another manager and you'll be in a much better position.
What usually happens here is that your most senior members of the team are picking up management responsibilities instead of doing IC ones. By all means they should contribute to mentorship, direction, culture, etc. but there is way too much going on to have a deep understanding of those 15 engineers.
The only times I think this work is when the leader sucks, so swamping them with reports means they have a more difficult time micro-managing. But they're probably getting in the way in some other fashion.
Concretely, managing 12 ICs on a well defined platform team w/ a single PM is much easier than managing 6 people working across 6 businesses, as is more common when managing a team of data scientists.
All my past experience disagrees. Sure you have 15 engineers, but you're supporting a business of 150 people. This is a pretty common ratio.
The noise gets very loud at that scale and it becomes almost impossible for self-managed engineers to make forward progress. At the very least you need super clearly defined ownership boundaries. That means business process and workstream ownership, not code ownership.