I Have A Choice?

I was paying my cable bill and noticed, below the amount I owed, they had an empty slot with the words "amount enclosed" just above.  So I checked and saw it was on other bills as well. Shouldn't they just assume the amount enclosed is the amount I owe?  Otherwise, why would I send it?

Or can I send in whatever I want?  Let's say the bill is $50.79 and I enclose $38.65--because that's what I felt your services were worth this  month.  Or nothing--screw you jerks.  Or some months I may feel generous and overpay, because that's the kind of guy I am.

I always thought bills through the mail are like going to the store--you pay the price they ask for or you don't get the product.  I understand credit card bills allow you to pay less than the full amount, but that's because they make their money charging interest.

So I'm wondering, are there people out there who just pay less?  I understand they'll eventually owe the full amount, but do companies put up with this from their customers?