What domestic device are you using that consumes more than 2.3kW? My vacuum cleaner with 900W is the most power hungry one I can think of. That is a pretty wide margin.
A 3kW kettle is the classic 13A appliance in the UK. I'm sure people would be keen to have a higher power version if possible, but lowering to 2.3kW would waste precious tea drinking time.
I've also got a 3kW plug-in electric radiator for emergency heat in the attic, but except for poor households in crap rented accommodation (lowest capital cost per kW and portable on moving) that's pretty niche these days.
