Hi, I know this post was a while back - just checking are you still running into this problem? Did you end up raising a case with Support?
Thanks for your question.
The ability to remove the Recents for all users is not available in Tableau Online. The reason for this is that you would need Admin access to rows in tables on a Server level. As Tableau Online is Site access on Tableau Server only, you will not have this ability.
I do recommend you to enter an Idea in this Community to gauge interest. Our Developers regularly check this section to consider it for a future release.
I hope this answers your question. Feel free to respond if it doesn't.