The service, if I remember correct was a full ISP experience were you could use it as regular internet in addition to playing games on it. It was to provide a "cheap" connection that was tailored for games but could be used for other things, but the hook was the optimised gaming.
Here is the wikipedia article which basically says the same thing.
SegaNet became a short-lived internet service geared for dial-up based online gaming on the Dreamcast game console. A replacement for Sega's original, PC-only online gaming service, Heat.net, it was initially quite popular when launched on September 10, 2000. Unlike a standard ISP, game servers would be connected directly into SegaNet's internal network, providing very low connection latency between the consoles and servers along with standard Internet access.[citation needed]
Online games on the Dreamcast initially allowed free access to their game servers, to be offset by SegaNet subscriptions and game sales. But with the demise of SegaNet, most games shut their servers down while Phantasy Star Online version 2 charged a monthly fee,[2][3] but was closed for the last time at the end of the year. There are some private servers still online that can be played with the following games: 4x4 Evolution, Maximum Pool, Phantasy Star Online, Quake III Arena, Sega Swirl (Using play by e-mail), and Starlancer.[citation needed]
http://en.wikipedia.org/wiki/SegaNet
The price Sega charged for the service was within the average price range of an ISP at the time, that is why there was no outcry. Unfortuntly at the time most people had their own service for going on the internet and the better latancy wasn't that much of draw to get the service.