I sometimes wonder why folks get so worked up about the "2kW fixed load" thing.
We all know the RFC is quite robust and tolerant of most things and many houses have (or had) practically everything bar the lights & cooker on a single RFC. Quite often folks would have a couple of 3kW heaters and the usual washing machine, tumble dryer, etc, in use and no problems.
Putting significantly more than 13A on at a point on the RFC is getting in to suspect territory as you can't be sure of how well the currents in the two "legs" are going to balance, but we have few loads that come in to that area. Probably just wired-in cookers, heating showers, or an EV charger in recent year or two, and they would normally be on separate radials anyway.
The only odd one I can think of is the old immersion heater, less popular these days due to combi boilers and instant-heat showers, as they would typically be around 3kW and could be heating for an hour or more easily. So were they the motivation for saying fixed loads above 2kW, and not the 3kW of a 13A socket?
Also the argument for putting something on to a separate circuit goes beyond the basic aspect of circuit protection alone, there is also the "good engineering" aspect of minimising inconvenience/risk under fault conditions to allow the fault to be isolated with the least collateral damage. I guess a number of "fixed loads" come in to this sort of territory, especially water heaters, where you would want to be able to keep any faults from taking out all/half of the house socket outlets as well.