People often say this without thinking about all of the details here. The largest power loads in your house (and in the world, period) are motors which are normally AC so you may not have as much of a benefit as you think.
Also, there are other small details to consider such as the safety of switches and plugs. When you disconnect AC it will arc and then self extinguish when it crosses 0V. DC will keep arcing longer than AC will making it a bit less safe. Just keep a lot of that stuff in mind.
Big appliances are already big, justifying putting an inverter on them if they can't be converted to DC. An inverter of appropriate size and power, of course, rather than a single mega one.
My argument is that this contest is a bandaid on an outdated way of thinking about power. Yes, safety is important. However, in your example we don't have to use physical-contact plugs. There are plenty of devices that can be powered or charged via induction.
Also, there are other small details to consider such as the safety of switches and plugs. When you disconnect AC it will arc and then self extinguish when it crosses 0V. DC will keep arcing longer than AC will making it a bit less safe. Just keep a lot of that stuff in mind.