If one has, say, 6 elements spread across three appliances, I would suspect that it is, in practice, statistically more likely that more will be 'on' simultaneously than if one had 6 elements in one appliance.
If all were being used how often do you envisage that all 6 would be heating simultaneously, and how long for? ... They cycle on and off which is part of the point with diversity.
Sure, that is 'part of diversity', but not all of it. As I've been saying, the reason for having multiple appliances, and the way in which they are to be used, is another factor in the statistical melting pot.
The point is perhaps clearer in extreme cases. Consider a kitchen shared by three people/households, with three cookers side-by-side (one for each of them), likely to be used at roughly the same time. Application of standard diversity calculations to each of the three cookers, separately, is fine - the result of those calculations being the postulated 'average' load presented by each appliance over a period of usage time. However, in that situation, I'm not sure that it is reasonable to lump all three cookers together and calculate a (lower total) after-diversity load. Put in more formal statistical terms, the legitimacy of averaging across all three cookers essentially relies on an assumption that the times that the three cookers are used are statistically 'independent' of one another. If all three users tend to cook at roughly the same time, that assumption of independence is invalid.
The reality, of course, that the 'safety margins' built into things such as the cable current-carrying-capacities of cables we work with are such that there will rarely be problems, at least as far as cables are concerned. I'm certainly not concerned about the cables. However, I'm perhaps a bit less comfortable with the prospect of the short-term 'overloading' of MCBs that can can result from 'generous' application of diversity (e.g. theoretically anything up to 80A or so, even if very briefly, through a 32A MCB).
Leaving aside diversity for the time being, cooking appliances often quote their total connected load, which is not the same thing as the total possible load, given that even where elements can not be energised simultaneously the manufacturers often add these together in order to achieve a more impressive figure. So a "3.6kW load" may actually have a maximum draw of 1.5kW for example.
Sure, the information provided by manufacturers can be confusing and misleading - and I certainly agree that, in terms of electrical common sense, all aspects of design should be on the basis of the
actual maximum possible current draw. However, as has been discussed, at least until next year, those electricians who feel constrained (by employers, insurers or scheme operators) to work strictly to the word of BS7671 are presumably stuck with having to follow "Manufacturer's Instructions" to the letter, even if those 'letters' are daft and/or inappropriate.
Kind Regards, John