Evidence:

1. The obsession with precise times in the last few chapters, the prominence of time-turners in the plot in general, and Harry's vow to revive Hermione all indicate use of time-turners in the final arc.
2. EY has involved many of his favorite ideas and themes (especially from the sequences) into HPMOR already. Timeless Decision Theory is without a doubt among his most prominent interests.
3. Harry has already gained two superpowers (super-patronus and partial transfiguration) by virtue of, well, being a proponent of EY's favorite themes essentially. Why not a third?
4. One specific concrete use would be to coordinate an indefinite number of selves in the way that Harry failed to during the prime-factoring experiment in the early chapters. Why did that experiment fail? Not because time is impossible to mess with, but because one of the Harry's messed up. But since then, Harry has been pushing the bounds of paradox. If he could firmly pre-commit to follow through on a course of action (perhaps with an unbreakable oath?) he could have an indefinite number of Harry's coordinate on some action. There are many ways this could be useful.