It's not a 4 set, that's just the human-readable formatting. The actual IPv4 address is an unsigned 32-bit integer. The human-readable format splits those into octets and displays them in decimal.
Your "add an octet" would result in using 40-bit integers, which isn't a normally used size nowadays. A variant of your idea would be to use 64-bit integers and simply double the size of the existing addressing, but this would break things the same way (as everything is predicated on dealing with 32-bit addresses), and going to 128 bits allows more future proofing and allows for some convenient auto-configuration methods, as you can stick a almost-always-unique MAC address (64 bits) into half of the address, then you can just stick the 64 bit network prefix in front of that and you've got a full IPv6 address ready.
You could conceivably write an IPv6 address in the same octets format as an IPv4, but it would be absurdly long i.e. 255.255.255.255.255.255.255.255.255.255.255.255.255.255.255.255, hence why they standardized on the "4 sets of 4 hex digits" format.