Mailing DVD rentals was literally what Netflix did before the advent of web streaming in the mid to late 2000s. They could offer a wider selection than Blockbuster, and people generally find it more convenient to sit around at home instead of putting on pants and going to their local video rental store.

While web streaming becoming popular (and the selection available for streaming becoming much wider) definitely dealt a killing blow to Blockbuster, Netflix was already successful with their mail-in rental service, and had made a name for themselves with it.

From what I understand, Netflix always intended to get into streaming. The DVD by mail thing was just a stopgap while the technology improved.