Naming people - can't reject sugestions

I don't think you have wasted your money.  In my experience, the performance, both in speed and accuracy of face recognition has improved between Elements 2020 and 2022. 

You say:

I have a large number of photos and so using the People page is not an option most of the time. There may be many suggestions, and the pictures when displayed are not clear enough to name people, and I am unaware if I can open the picture with the suggested name to confirm.

In my opinion, having a large number of photos is the perfect reason to use the UnNamed People page.  I would say that in 90% of cases, the stacks contain only a single person. In Elements 2022, I have had several hundred photos in a single stack.  Naming the person identified in the stack is a breeze compared to naming faces individually in a single photo.

• If you are using the Faces view of a stack, you can hover over a face and a large thumbnail of the photo will pop up;
• If you use the Media view of a stack, a slightly smaller thumbnail of the photos is displayed;
• If you double-click on either a face or a photo, it will open up a media grid with a zoom control that lets you see the photos up to single image view.  (Click the back button in the top left of the window to return to the UnNamed People page.)

Any of these options should allow you to quickly confirm whose face has been recognized in a particular photo.  For this reason, I name people almost excusively via this method, which is why the bug you raise doesn't bother me at all. 

As far as I am concerned, this is a random bug.  The only solution is to reject all of the incorrect suggestions in the People room (using Not this person) rather than in the Media grid.