Now, latency is a slightly different issue. I would suggest that it's reasonable to either run an extra line OR host some servers locally to deal with that.
How does running an extra line lower your latency? I think you're confusing bandwidth and latency here. Latency would involve replacing your line with better infrastructure (small impact) or changing the route your packets would tend to take to one with fewer hops and shorter distances (big impact).
If your latency is generally a combination of # of routers, physical path, and network congestion between you and the destination. Locally number of hops dominates the latency. So if the old path is comcast > Level 3 > google then running a comcast > google line will lower your latency by removing Level 3's routers and probably proving a shorter path.
Bandwidth isn't literally width like a pipe of water. It is linespeed. That is why higher quality cables have higher bandwidth, even though packet transmission is completely serial. "wdth" is an illusion created by time division multiplexing, like multitasking/multithreading on a PC.
This isn't always true because time isn't the only multiplexing strategy used. For instance, modern cable modems use code-division multiplexing, and fiber optic communications typically uses a variant of wavelength-division multiplexing. In both of the later cases, there is actually simultaneous transmission.
How does running an extra line lower your latency? I think you're confusing bandwidth and latency here. Latency would involve replacing your line with better infrastructure (small impact) or changing the route your packets would tend to take to one with fewer hops and shorter distances (big impact).