Yes you are correct.I have seen many times a shower on a MCB technically too small, and I would guess a 16 amp oven would run on a 13A fuse, however I would not say that is the way it should be done, diversity is size of largest device then percentage of others, so if one set of heating elements is 3.5 kW then in theory should not be on 13A fuse.
But the manufacturer of my cooker says full load 65A but still says supply from 32A MCB/RCBO.
I have often seen/been party to running 4KW of stage lighting on 13A fused plugs but it's not right.
A 10.5KW shower on 30/32A OCD and 4mm² cable is also very wrong but it works and I came across one a while ago but customer refused to change it as it had been working troublefree for a number of years without signs of melting/scorching. I informed the freeholder and hope it got followed up.
My daughter's range quote 14.7KW max MI and suggests 32A to 45A [7.4 to 10.4KW] supply depending on usage.