An advantage to be sure. But that doesn't explain why Union soldiers didn't abandon the Union cause in droves when their enlistments ran out in the spring and summer of 1864. They did not, in overwhelming numbers.
The tide had turned by that point and most of the hard slog was behind them. They probably felt they were going to win and wanted to be part of the win. Additionally, what would they do for work? Would people look down on them as quitters or even deserters if they were not fighting for the heavily propagandized cause?
The best time to be in the army is after the heavy lifting is already done, and for some people it gives them a sense of belonging so many make a career out of it.
I've known a lot of career army people. Some love the order it imposes on their lives.