The two advantages are that you avoid the discomfort and time of haggling in-person, and the person responding to internet offers plausibly has more of an incentive to acheive high-volumn sales, rather than high-price.

The third -- a rather major -- advantage is that negotiating through email is efficient enough for you to negotiate with multiple dealerships simultaneously and, in particular, play them against each other. Phrases like "I am talking to a few other dealerships and your price is not competitive" are highly useful.