If I remember correctly there was pre-qualifying up to the 90s/2000s
But back then Le Mans was not part of a championship so did not have to keep to entry requirements.
Easy solution: Build more pit boxes and allow more cars to enter :P - joking aside considering the length of the track and the professionalism of modern teams(they are miles ahead to the average back of grid teams from even 15 years ago) , I guess the track could fit 5-10 more cars without much issue.
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