If I'm doing a recipe with no pattern, few sugars, and I really just want it to saponify and trace quickly, I'll soap at 115-130°f.
If I want time to swirl with my normal recipe that doesn't heat up and has hard butters, I'll soap at 105-120°, maybe a little lower if I'm throwing honey or sugar in it.
And if I'm doing a cider or beer soap with a FO that also heats up the soap, I'll wait for the 80-95° range before soaping.
I'll also soap a little cooler if I anticipate adding more liquid than normal, since that can also contribute to heating.
I believe the "waiting until lye and oils are within 10 degrees of each other" is to help you correctly pinpoint the temperature you began soaping at. Soaping hotter or colder can influence how your soap will behave and the reasons it might thicken. If you misjudge how much one temperature will affect the other, you might need to change your plans, just depending on how the batter is responding.
If someone knows of another reason for that rule, I'm happy to hear it.