Other than speed, is there a reason that a 10W iPad charger shouldn't charge a new MacBook Pro 2016?
A 10W iPad charger should in theory work and you would be correct that it would be a slow charge.   Well, to be accurate, it would be a horribly slow charge - you are getting a charger that is 1/6th (17%) of what is required (61W).

Will there be a problem?  No.

Will it charge?  Slowly.  Molasses in January slowly. From Apple's web site:


  Your Mac will charge from USB-C power adapters not manufactured by
  Apple if they adhere to the USB Power Delivery specification.


Assuming you are using a genuine Apple iPad charger, it should charge since Apple charges adhere to the spec.