...Although for a large part, the different components of that ship were designed separately, and often to cross-purposes, so that the task of integrating them into something resembling a ship-shaped object, let alone a working starship, was immense.
As for the size of the rec room, TOS already makes mention of rec facilities up to "Rec Room 6", and indicates that Rec Room 3 is at least three stories tall. TAS shows a giant virtual reality bay as being part of the rec facilities - perhaps replacing most of the previous facilities, or at least the big Room 3. Perhaps this cavern is later replaced by the TMP facility - or perhaps the asymmetrically placed TMP rec hall is paired with a holodeck on the port side of the saucer, a windowless facility?
Timo Saloniemi