You would not be putting false trust in a fuse that might not be providing protection. I happily use my 13A plugs but I know that the fuse will not make an appliance safe if the polarity is reversed or if I am using my inverter.And if that appliance had a continental plug on it, how could that be safer than your 13A plug?
Ian
In practice the plug fuse is probably not the weakest link. However a single pole switch on the socket is different matter, there is a documented case of a canal boater electrocuting himself because he switched an appliance of at the socket switch and then got a shock from the appliance. Luckily he survived to tell the tale but if there had not been a switch he would have unplugged instead of putting his trust in a switch that had only turned off half the supply from his inverter.