They didn't take over immediately (it's a pain to change email addresses, the lock-in is pretty high), but they did force nearly immediate changes from the major players. Hotmail at the time was offering only a few megabytes of storage (!) while Yahoo! was offering 6MB. Within months both providers greatly increased their storage, though not immediately to the level of Gmail, to help retain users.
Agreed. I think this is a pretty good example of competition and market forces causing all users to have an improvement, even though the vast majority don't know or care about these things.