> why would a single player game need the web to work
For the same reason Siri needs a connection to work: there's a lot of heavy processing going on, which your client device just couldn't handle even if it wanted to, that is being offloaded to a cluster somewhere instead. In Siri's case, it's linguistic analysis; in SimCity's case, it's inter-city traffic-flow, economy, and other expansive high-granularity world-simulation tasks.
...or, at least, that's what EA's engineering claimed at some point. To still be charitable to them, but to temper this with pragmatism a bit, I don't think there's really that much difficult processing going on; I imagine it was more that high-end gaming PCs could run everything client-side, but the low-to-medium-end PC market--from which Maxis pulls the lion's share of its sales volume--couldn't.
Shoving the processing server-side means everyone can get the effect of throwing a 3GHz Xeon at their world-simulation, and the total amount of processing required can be decreased dramatically by using player's real cities to neighbor other real cities for inter-city world-sim calculations, instead of having to simultaneously synthesize the behavior of 8+ AI cities to interact with each real one.
To put it another way, I imagine it would be very hard to market a game where the core feature ("new, more granular, more realistic simulation!") degrades into non-existence on the average PC, thus rendering an upgrade from the previous version moot.