Given the age of this thread, it is probably good to provide some additional information about your situation, especially since the OP never stated what MS products were installed on machines.
So, what version of Pro are you using now? What version of MS Office is installed (if any)? What driver, specifically, are you installing/reinstalling?
Im running windows 10, the current version of arcGIS (the 64bit version on the current downloads page) and i am following the link to the microsoft 2016 Database tool that pops up in the error message
I'm currently facing the same issue though I never had it before since I had already installed the driver. I've reinstalled it (numerous times) using the recommended ways yet I still receive the error.
Any success with the issue? I'm using ArcGIS Pro 2.7 (2.7.3).
I am having the same problem with ArcGIS Pro 2.8.2. I didn't have this problem before I installed the last update. I am not running a Python clone. I have tried other Excel files and even tried to import them into ArcGIS Online. Something must have gotten broken in this last update.