A state must have a monopoly on its money. We don't let people print money and cards are an indirection, but they must still deal in US currency. The note is the most basic form of that currency.
So yes, you should need to count 1,000 pennies. You might not like it .. it may be abused, but those are the rules of the system we currently have.
There is, however, no Federal statute mandating that a private business, a person or an organization must accept currency or coins as for payment for goods and/or services. Private businesses are free to develop their own policies on whether or not to accept cash unless there is a State law which says otherwise. For example, a bus line may prohibit payment of fares in pennies or dollar bills. In addition, movie theaters, convenience stores and gas stations may refuse to accept large denomination currency (usually notes above $20) as a matter of policy.