I don't think a manager will be impressed by a report saying "I know you can't do your whole job, so let me handle face time with the execs so I can take your job from you."
If I don't trust them to represent me and the team, then obviously that suggestion wouldn't work, but I'm trying to express the difference between someone pointing out a problem as if the problem is just yours or offering to help take responsibility for the problem as part of a team with you.
I've worked with people who made it a point of pride to always bring a concrete, workable suggestion whenever they brought me a problem. We didn't always go with their suggestion, but they were fantastic to work with.
Thankfully, I've never had to worry about keeping good people on my team down out of fear they'd take my job.
It's funny because it could go exactly the two opposite ways. If you "report the problem", you might be - totally as punishment - volunteered into the position to work on it, in addition to your normal workload. If you "report the problem and volunteer to do something about it", you might be shot down. Hilarious, right?
That's back to the fundamental problem: you need to work on building an understanding of your manager. You have the workload assigned to you, then you have everything you need to do to further your own career.