This is not a problem for GA. This is CASA's problem.
There is no rule that says a pilot has to KNOW exactly what his takeoff distance will be. There is also no rule that says he has to DETERMINE his takeoff distance prior to taking off (or how he must determine it).
Sure, there is a great big rule that says he must not take off overloaded, but to satisfy this rule does not necessarily require him to know what the takeoff distance will be.
So, most people will then say, "but how does he know that he has sufficient runway if he does not, or cannot, consult a chart?".
And the answer to that question can be something like, "I know from experience that I have sufficient runway." He could even say that he has consulted the local clairvoyant, or done a reading of his tea leaves.
The point is that it would be up to CASA to prove that he did not have sufficient distance available when he commenced the take off roll. This is where it becomes CASA's problem.