Many ≤3kW ovens and ≤3kW electric heaters do, indeed, come with fitted 13A plugs and get used as such. Although it is 'OK' (everything being used within its ratings), I personally am more comfortable having 'fixed wiring', rather than a plug/socket, for loads that high.That's what I did. A different oven, but similar rating, so I used a 13A plug. .... Isn't it normal practice to use a 13A plug for a 3kW electric fire? I've done that before now.
One of the theoretical issues is that it is said that the 'wiping' of pins and contacts of 13A plugs/sockets when the plug is inserted or removed which helps to keep the electrical contact surfaces 'tarnish free' (hence improving electrical contact). A plug on an oven may well not be pulled out of the socket for literally years.
Kind Regards, John
Good point. But what would happen if electrical contact became less efficient? Arcing? Over-heating?
(A genuine question; I am not an expert.)