I know plenty of academics who are highly engaging in writing but utterly useless at speaking -- even in private conversations, never mind public speaking.

I feel sorry for their students, but I'm glad for the books and research they produce.

Do you know of any who were able to improve their speaking? If so, do you know how?

For very famous ones, yes, but it drops off pretty quickly. For most authors, the speaking gigs tend to be unpaid--- travel around the country doing book readings and such to promote your book. An exception can be nonfiction authors who can get onto the corporate workshops circuit, but my guess is that novelists aren't too much in demand there.

I can't imagine that a significant number of people would be able to earn significant amounts of money by speaking.

Only if you're Malcolm Gladwell.