No one has commented, so I will add some speculation from an engineering/manufacturing standpoint.

Flat topped helmets would be easier to make if metal is accessible in thick sheets. Instead of hammering out a more complex concave shape like a bowl, one can form most pieces with metal rolling equipment and then rivet the parts together. If an armorer already had to flatten their own stock by hand, though, then curving it into a desired final state is not an appreciably longer process.

Now, did their rise of flat top helmets coincide with the advent of sheet metal and metal rolling technology? I honestly have no idea. I would love to hear any alternative thoughts, though.