I know little about locomotive efficiency, but it seems plausible that it takes less energy to accelerate a cut of grain cars to 9 mph than to 19 mph, even if 9 mph is not the most efficient speed at which to run the locomotive.
The most efficient thing should be to not have to accelerate at all. Unless the train is going to go 10 mph for the hundreds if not thousands of miles that it will travel, the train will have to accelerate to deal with this one bit of crappy track. Sure it should take less energy to go from 0 to 9 than from 0 to 19, but if 9 mph is less efficient to run at for long distances than 19, the train will take a loss on efficiency. Accelerating your car from 0 mph to 1 mph is much easier than from 0 mph to 40 mph, but 40 is a much more efficient speed than 1 if held constant for a long trip.
The train is cruising along at speed, and then as the train approaches this piece of execrable track, the engineers have to jam on the brakes, ride the rail at 10 mph, and then waste fuel accelerating back to whatever normal speed for that train is. Acceleration is very detrimental to fuel economy, the lower mpgs of a car which tailgates and weaves between traffic, braking and accelerating to gain a few car lengths as compared to a comparable car driven constantly at the speed of traffic helps show this.
Would track improvements on a branch line pay for themselves in greater turnover of grain cars, decreased fuel and labor expenses, etc.? I imagine that the railroad has crunched those numbers carefully, and if they haven't improved the track, it's because the answer is no
The answer to your questions is clearly "yes". When trains can move faster, more of them can move through a route in a given amount of time. Less acceleration equates to better fuel economy, and even a constant 10 mph may be less efficient than whatever speed the train normally would run at. When trains complete their routes faster, the crew is on them for less time, so that cuts down on labor expenses.
I'm not willing to jump on board the "people who should know more than I aren't doing the common-sense solution, ergo that solution is wrong" bandwagon, as corporations have a tragic recent history of putting short-term profits above long-term profitability...and common sense.
Remember that they have a captive market, since it's cost-prohibitive to ship grain by truck, and there aren't any other railroads to offer competition.
Yes, they do pretty much have such a hold on their market. However, instead of exploiting that advantages of that hold to maintain the status quo, perhaps they could invest to make even more money down the road. If improving the rail allows them to charge the same amount to customers, but cost the railroad company less per train, then the company wins. However, the company would have to incur the short-term large expense of track improvement, and they're not going to do that. Corporate boards as a whole need to get some glasses as they all seem to suffer from extreme myopia.
Sometimes I wonder if Jim Taggart does exist, and that he really is a railroad CEO, because it seems like it.