It does depend on how far the point where your tapping into the ring is from the consumer unit. If central then no real problem any overload will trip the consumer unit trip so fails safe. However there is a directive in the appendix which suggests over 2kW you should use a dedicated supply. The problem is if you have a load of high loads towards one end of the ring then one leg can exceed the 22A limit before the other leg hits 10A so one leg can become over loaded before you reach the point where the MCB will trip.
Small items like a kettle are not a problem because the time it takes to boil is short, an immersion heater is a big problem because it runs for a long time. Although it says fixed over 2kW in real terms the dishwasher is OK because the heater is used for such a short time, and tumble drier or washer/dryer is nearly as bad as the immersion heater.
The over does depend on type, most do not take long to heat up, so soon start to cycle, but there are some which do take power for an extended time, the range type for example.
Also any fuse gets hot, it's how they work, so any fuse holder must be able to get rid of the heat, a fused connection unit (FCU) puts the heat into the wall, and can in the main get rid of heat better than a plug (with a fuse inside), a plug should be in free air, although where the oven fan cools the plug there is no a problem, but putting a 13A socket where the plug will not get cooled is a problem.
With a dedicated supply since the MCB will likely be 16A it does not need a fused plug and nothing to stop up using a 15A socket and plug which are not fused, it was common at one time to use them in the airing cupboard to feed immersion heater, no fuse so no heat.
I am not saying you can't plug an oven into a ring final, but if you do the loads should be considered.
