I don't know if it's unreasonable, but it's definitely unrealistic.
 
I can't remember a tournament I've bowled in where they pair groups of bowlers by average, be it scratch or handicap, professional or amateur. I'm not sure why it should matter.

That would give you an unfair advantage.  Some bigger tournaments have divisions to ensure what you want happens... But what happens to luck of the draw?

Last weekend, I was paired with with the (after viewing results) 3 of the bottom 10 AE final scores, and I ended up 3rd all events..(city tournament.. Bowled it with my pops )...

I prefer when I get paired up with people who are better bowlers than me. It actually makes me bowl better because in my mind I see them as the competition and I don't want to get embarrassed and blown out of the water.

Yes!!!!!! Me too!

The short answer is yes.
 
Are we talking THS? And you are worried about how to break down the lanes properly? Did it ever occur to you that having that person throwing plastic may have helped you? If they drag the oil down inside of where you were playing, they just created hold for you. When you bowl in your leagues...do you only bowl with people of your same average? Do you whine and complain if you bowl against a team of lower average bowlers? Why do it here?
 
And if this isn't THS, the arguements are still the same. If this is a local, city, or state tournament, everyone has the right to bowl. What if in the squad you were the highest average by 20-30 pins over the next person, should you just not bowl? What if in your squad there are 20 bowlers at your average...but when I bowl we get the first scenario, is that fair to me? The fair thing is a random draw, and everyone bowls with whoever they get. If this tournament is open to everyone, why should they cater to you or to any higher average bowler?
 
Remember this, without the guy throwing plastic, and the rest like him, the prize fund goes way down. Pretty soon, you will just be playing with yourself, and that pun is very much intended.