I believe that good HR and L&D teams can be a huge critical advantage for large organizations. Unfortunately, there are too few of these good teams. Small and medium sized companies in many cases can't even afford substantial HR and L&D teams.
Regardless of your situation, don't delegate too many tasks to HR and L&D. You need to maintain control for things like hiring, development discussions/plans, performance management, etc. If you don't, you won't like the results and you will still be held accountable for them.
If you have a good HR and L&D team, utilize them as a resource, but own the tasks for your team. The benefits outweigh any time concerns.
P.S. - If you HR and L&D teams really are good, they will tell you the same thing and have the solutions to make you better, but not delegate those key tasks.