Does a backsplash need to meet the counter on it's face?

Dee W
by Dee W
We are updating our kitchen and installed a counter with a small backsplash. DH intends to add a glass backsplash on top ot the wall lip to the bottom of the cupboards but I have never seen it done anywhere.
Would it work out alright or Is there a valid reason I can give him not to do this?
The lip is easily seen here
Another view as we were installing the countertop
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