For the moment forget it being a boiler, it is a fixed appliance, unlike a portable appliance the manufacturer can stipulate the protection required, I have installed fixed appliances where it required semi conductor fuses, because it's fixed the manufacturer can stipulate the protection required.
I would agree engineering practice is where the fixed appliance powers some thing external then internal components are internally fused, since the pump, time clock, thermostat, motorised valve and other items are also powered from the same fuse, it would seem daft to rely on it to protect the boiler electronics, and the 3A fuse is not really good enough.
However the question was also FCU or plug, the problem is more likely a plug is removed when the boiler is running than a FCU has the fuse removed while the boiler is running, so there could be a problem in the way it is turned off, same applies with a built in oven, it needs to cool down before it is disconnected. However a do not remove sign likely does the same.