There's considerable losses involved when you want to convert between frequencies. DC also has considerable losses over long distance, so there's a lower bound on the frequency before the efficiency starts to go down again.
The losses over distance thing is the fundamental conflict between desired properties. For transmission you want as high a voltage as possible, but high voltage is both very dangerous and tricky to contain. So for residential use you want a much lower voltage. we picked ~ 200 volts as fit for purpose for this task. but 200 volts has high loses during long distance transmit. So having a way to transform the current into voltage is critical.
Some of our highest voltage most efficient long distance transmission lines are DC, but this is only possible due to modern semiconducting switches.
quadratically