Wing root mounted guns have the problem of reduced ROF due to the need for synchronization, combined with the problem of reduced roll rate due to the mass being off of centerline (although to a significantly lesser extent than guns mounted further out in the wing).
Also, depending on what you are designing the airframe for (say intercepter vs LR escort), there is the problem of fuel tank placement. If you need to use space in the wing for fuel stowage, then wing root mounted guns would require that the fuel tanks be further out in the wing, causing problems with roll rate. This outer wing fuel tank problem could be reduced somewhat by using the fuel in these tanks first, so that by the time you reached the combat area the tanks were empty. But if you can not count on fighting at a range from base that would use up this fuel, the roll problem remains. This is one of the reasons that wing fuel tanks were usually placed close to the fuselage in fighters, another reason being that the wing is usually thicker there, which makes it easier and more efficient (in terms of both tank weight and volume) to install the fuel load there.