This was an issue of bad timing, not a bad business model. People weren't really mentally at the point of buying such thing on-line, and pets.com burnt through their cash so quickly that it couldn't wait for people to start adopting it. As pointed out by others, Amazon made it work; however, they are very smart about diversifying, re-investing, and not being profligate with cash-on-hand.
Edit: Not such a good idea in 1999, when operating without economies of scale and scope, and with high transportation costs.