Why is there no DC standard for household wiring
Nowadays, we could have 230V DC as the household wiring. Modern mains adapters actually rectify the 230V 50Hz AC to DC, then make 10kHz AC out of it, transform it to e.g. 12V AC and rectify it again.

BUT, there is still one big disadvantage of DC in that system. Maybe your grandmother still knows about the old times, when DC in households was still common: The switches need to be spring-loaded, because DC has no zero-crossing and so, arcs lighting up during switch-off a loaded circuit will not extinguish automatically. Same for plugs and receptables, you don't want to accidentally pull a loaded 230V DC 16A plug.