Let's say you wait at lights/intersections for 10 minutes during your ride. If you average 13 mph when moving (that includes accelerating and decelerating at stops), then you will arrive in around 40 minutes total time. At 16 mph, you save 5 minutes. Bump it up to 18 mph, and you save 8 minutes. To get to an 18 mph average, you would need to be going at least 20 at steady cruising speed. It might not even be feasible to sustain that speed consistently in the traffic conditions you are encountering.
With real-world commuting, especially in a metropolitan area, the bottom line is that as you get faster, the route itself becomes the limiting factor on your overall time. Over time I've experimented with my route to find one that minimizes the time spent stopped.
A different bike, with better aero or geometry or just being lighter, isn't going to get you much more than a couple of mph, which translates to a few minutes in reality. I would say if you try another bike and enjoy the ride more on it, then it's worth getting. The more you enjoy, the more you ride, and the faster you'll get.