You are right- it doesn't make much sense to counterfeit dollar bills. A typical counterfeiter passes the bills themselves by store purchases, or possibly sells bulk bills to a distributor. But who would buy large amounts of $1 bills? A business that would pass the bills when making change? Seems like a lot of risk and effort for little gain. Using the bills as a means to spread a toxin would probably work, since drug residue, for example, from cocaine, is transferred in that manner.
The risk would be in passing the notes. What are you going to do with large amounts of $1 bills? The more transactions required to get rid of counterfeit notes, the higher the chance is of being caught. Eventually, they have to be spent somewhere on something.