There are a lot of examples here of where that would fail (openings, checks). Would it make sense to introduce rules like letting people pick any move they want

There are a lot of examples here of where that would fail (openings, checks). Would it make sense to introduce rules like letting people pick any move they want for the first three turns, or allowing any checking move and counter-checking move? Or is that one of those situation where trying to fix an obvious problem lead to move issues with defining the problem clearly?