Would it need a larger supply, then, probably no.

People have lived in typical houses with all electric heating and cooking for 70+ years with no detrimental effects on the incoming 60 or 80 amp fuse.

The actual loads used are nothing like the figures you have used for diversity, if lighting was using 8 amps, they'd be running a 24 hour office environment. The total wattage for lighitng in my house will be around 130 watts, less than an amp, and that use is for less then 6 hours a days for individual rooms, so if averaged out, a load of <5 watts for 24 hours.

Sockets are the same, rated at 20 or 32 amps, but actual use is very low. The biggest draw in most houses will be the kettle. Ovens are intermittent, even electric heating is intermittent use. Storage heaters draw a large (10 amps?) load at start up, but this is usually when nothing else is being used, so not a large load overall on the system.

Water heaters, where is the 45 amps from - a shower? Intermittent use. Immersions are only on for 2 hours from cold, so again, limited intermittent use.

Yeah, lights and sockets are realistically lower, but if its cold in winter and the electric heating radiators are all on (25A or 60A), then you have a shower (44A), someone is in the kitchen cooking (17.5A) and uses the hot tap to wash up (24A). That's probably the worst likely case and the true maximum demand. I'd prefer to keep it single phase but obviously it needs to be correct and safe.

Yeah, lights and sockets are realistically lower, but if its cold in winter and the electric heating radiators are all on (25A or 60A), then you have a shower (44A), someone is in the kitchen cooking (17.5A) and uses the hot tap to wash up (24A). That's probably the worst likely case and the true maximum demand. I'd prefer to keep it single phase but obviously it needs to be correct and safe.