That was part of it. Obviously if sites had no choice in the matter then it wouldn't have mattered whether browsers enabled it by default or not.
Since it was a voluntary thing though, browsers sending it by default pretty much destroyed what chance there was of mainstream sites deciding to implement support for it. It's one thing to give up on tracking a small portion of users who explicitly opt-out, and another thing entirely to give up on tracking everyone except for a tiny minority who choose to opt-in.
