Virtually all proposals for central bank digital currencies (CBDCs) include a provision for account limits. They are meant to protect the regular banking system from bank runs into the CBDC, and for this reason, they are likely to remain a permanent feature. We argue that account limits are at least practically not compatible with smart contracts like those offered by systems like Ethereum. This means that CBDCs will likely not be able to offer the same extent of programmability features as blockchains.