I hope this makes sense!
It doesn't in a dedicated cooker circuit when it's hard-wired.
The fuse is required when it is plugged into a socket circuit, because (very simplisticly) plugs have space for fuses; there are usually other appliances plugged into a ring main taking power; sockets and plugs are tested to sustain a certain current for a set period of time; and the mechanism for a plug and socket to make an electrical connection can have far more resistance than an undisturbed screw terminal.
These are all factors that you would want to limit the current for, with a fuse.
As an example, I could buy a 3.5kW oven, that has a maximum current draw of 15A. This is only just over the 13A of your hob, but I don't think anyone would question that it couldn't be hard-wired to a 32A cooker circuit.
And as for fire risk - a normal failure mode for an appliance, may be a short circuit. As V=IR, any electrical short could, for a brief moment, create a massive over-current; this would be enough to blow most fuses, be they 3A or 32A!
In the worst case, if there were some sort of fault that could cause a near short, for a sustained period (extremely unlikely), then yes, a 13A fuse would break sooner. However, there would still be little fire risk, as that over current would still be within the capabilities of the (possibly) 6mm² cable used on the cooker circuit.