I couldn't manage it without the carbs - didn't have the energy to work out properly.
However more importantly once you have saturated your body with protein, eating more like you need to do to build makes some of it convert to glucose which takes you out of ketois. Then you are basically on a very high fat diet, not in ketosis which is not a very desirable place to be.
Depends how reliant you are on the Keto diet to manage your bloods, i have been doing well on a low fat, much lower carb, higher protein diet. But i can process things like lentils and beans - even smaller portions of pasta and bread without my blood levels rising out of tolerance now i have lost of a load of weight and got fitter.
What ever you choose to do, make a slow change and test your bloods. You may find if you keep high fat and up protein allot you will put on all the wrong kinds of weight.