I use the same weight broadhead as field points and I bare shaft tune until I know I have the right weight field point. Once tuned I've never been able to not just swap the same weight broadhead for same weight field point and have good arrow flight.
I don't think I agree with the reasoning on the broadhead causing the arrow to act weaker. The overall length might be slightly increased, but the bending portion of the shaft is the same. There might be a slight (miniscule) increase in FOC but I don't think there's going to be a noticeable change in the dynamic spine of the arrow. If there is I've never noticed it.