Of course they don't. I'm speaking of $1 bills in particular. One of my geek hobbies is Where's George? No doubt you have received a bill with some Where's George markings on it, directing you to that website so that the movements of that bill can be tracked, for kicks and giggles.
In some of the budget cutting talks this year, the discussion turned to eliminating the $1 bill and replacing it with a $1 coin. This makes a lot of sense. Coins are vastly more durable than paper money. Did you know the average $1 bill only lives about 18 months? Over the long run, the cost savings are enormous- $5.6 billion over 30 years. This makes it worth doing.
But, but, but.. my hobby! Well, screw that. Nobody owes me a hobby. Where's George will as easily become "Where's Tom?" as $2 bills become the new smallest paper denomination, or, "Where's Abe?", as the public doesn't generally like $2s.
I'm fond of pennies, but there's really no good reason to continue minting them. I like riding trains, but that doesn't mean I support subsidies to Amtrak. Etc. I don't expect the entire country to spend foolishly just so that I may continue to enjoy a hobby as I know it today. My whims just aren't that important.
So, if the $1 should fade into history, I'll be glad of it overall. I'll smile at the cost savings to my country, and adjust my bill stamping habits accordingly.