It supported billions of addresses, but only millions of networks. The registry could only give out 128 16-million address chunks, 16,384 64k chunks, and ~2M 256 address chunks.
IPv4 was running out of class B's, those 64k address chunks, when CIDR was introduced.
> Addresses are fixed length of four octets (32 bits). An address begins with a network number, followed by local address (called the "rest" field). There are three formats or classes of internet addresses: in class a, the high order bit is zero, the next 7 bits are the network, and the last 24 bits are the local address; [...]
7 bit network times 24bit local addresses is already more than two billions.
[0] https://tools.ietf.org/html/rfc791