I was always under the impression that the dilithium crystals acted as a transformer or converter (it was referred to as the "dilithium crystal converter assembly" several times), somehow channeling or altering the raw energy from the matter-antimatter reaction to produce the warp field.
. . . As I see it, one thing serves as a power source and another regulates the power consumption/reaction; never both with one thing. But in TOS, the concept doesn't ever seem to be very clearly defined . . .
BTW, apparently you can buy the stuff at Wal-Mart!