All motion relies on the integrity of our mid bodies, so if you are really going for a heavy leg workout you may want to warm up the core body but not fatigue it so that it can have enough energy to maintain a secure position while working the lower body
Another option would be to work the core on a day when you can work core and back and leave the legs out of it!
Hi Leila. I noticed that your question says “fatigue” the core before a “heavy” leg workout. I added the emphasis here because that is what I’m limiting my answer to since I believe it’s perfectly fine to “work” the core prior to or in conjunction with a leg workout. But, as you identify here in your question, FATIGUING the core prior to a HEAVY leg workout would be problematic in my opinion because of the importance of the core to heavy leg workouts—PARTICULARLY the type of heavy leg workouts that you identify in your question (namely free weight workouts like squats and lunges). Assuming that you are speaking of free weight workouts with the legs, the importance of not pre-fatiguing the core prior to the leg workout is even more dramatic since it is your core that will be providing the all-important stability to the exercise.
So the answer as to why NOT do this would be for two primary reasons, FIRST, and in my opinion most important would be for safety reasons, and SECOND would be for performance reasons.
I hope that this helps.