It’s possible to regret having too FEW teeth in your mouth, but what about the opposite: would someone regret having too MANY teeth?

I had three too many wisdom teeth. Had to be cut out of my jaw below the gum line, there was no room for them.

Yep.
I had a similar issue to Slartibartfast.  They had to remove my "wisdom" teeth.

Funny story, when they gave me the IV to put me under, I started counting backward from 100 ... 99 ... 98 ... {out}.
Woke up ... 97 ... 96 ...

"What are you doing?" asked the dental assistant.
"They told me to count backward from 100." I replied.
"Oh.  You already had the surgery."  she told me.  Sure enough, I looked at the clock and had been out a little over 2 hours.
She helped me to a recovery room ... and I hit on her 'cause she was cute and I was still under the effects of the anesthesia.

lol

I don't have that problem. I recently had sinus lifts (bone grafts) in preparation for getting implants early next year.

I'm sure that is true for some.  Dental problems of any kind are a hassle for sure. 

Too few is not generally a problem unless it's WAY too few.