I will be a bit of a naysayer. If you were hitting it pretty hard every day, then I would think a day of rest is a great idea.

I would guess that 10 miles takes you no longer than an hour? If the level of effort feels moderate to you, then I am not sure why you'd need a rest day (or week).

Unless you are really grinding out those 10 miles a day, then I wonder if you should check that your bike is fitted correctly. I would be worried that the fit it causing issues with your legs more than the level of effort.

Let me be very clear that I am not making some macho man claim about that I ride a century a day or nonsense like that. If the riding you do is a hard workout for you, then a rest day would really help.