What are the curved centerlines at taxiway intersections for?
The line along taxiway centreline is meant to provide guidance before initiating the turn. You're right that in a large aircraft they would lose sight of the centreline when they're over it, but it gives the pilot an idea of where they need to keep the nose in order to keep the outer main wheels behind them on the taxiway surface. 
For example, in Canada, Transport Canada document TP312 (Aerodrome Standards and Recommended Practices) define how you need to place the centreline in order for the outer main wheels to remain at least a certain distance from the taxiway edge. (I believe the United States would have very similar rules; I just don't know the names of the appropriate documents)

Taxiway Curves
3.4.1.6 Recommendation - Changes in direction of taxiways should be as few and small as possible. The radii of the curves should be compatible with the manoeuvring capability and normal taxiing speeds of the aeroplanes for which the taxiway is intended. The design of the curve should be such that, when the cockpit of the aeroplane remains over the taxiway centre line markings, the clearance distance between the outer main wheels of the aeroplane and the edge of the taxiway should not be less than those specified in 3.4.1.3.

Think about when a large aircraft has to make a big turn (&gt;90degrees). If there was no indication on the surface about how to take the turn in a large aircraft, you could inadvertently take it too early and run the main wheels off the pavement.
Here's an example of an aircraft following the centreline with its nose as best as possible in order to keep the main wheels in the right spot.