Having a fuse in the plug is very good for safety because the circuit breaker in the house will be too large to provide adequate protection for the cable and equipment connected to the plug.
But that is only true in the UK because of post-war copper-saving, where pairs of 15A radial circuits were allowed to be joined together to form 30A rings. In most of Europe, sockets are wired on 16A circuits, which actually provides better protection against flex fires than a BS1363 plug with 13A fuse. (Because a 16A MCB breaks faster for small overloads than a 13A BS1362 fuse, and because the breaker is for the whole circuit, not just the faulty device.)
A BS1363 plug with a 3A fuse theoretically provides much better protection for the flex. But the user might not fit one. In any case, harmonized European regulations do not permit appliances to be sold with thin flexes that could not carry a 16A fault current for a short time.
Being non-polarised is bad because the live wire could be connected to either conductor so class 3 equipment will need two fuses to protect it against short circuit and the switch will need to be two pole to isolate the appliance from the mains.
Class III is SELV. All appliances, even if polarized, should treat the live and neutral as equally hazardous, since the neutral becomes live if it is accidentally severed upstream. Having two fuses would be pointless since you do not know which will blow first. Unless you are thinking of a fault to earth in a Class I device, in which case any fusing does not matter as long as the earth conductor is adequate.
The shutters on UK sockets are a nice feature, though arguably only necessary because of the huge pin sizes. But the system has bad points too. The risk of foot injury. The fact that if the plug is smashed or comes unscrewed then live parts are exposed and it is very difficult to remove safely. (Rewireable plugs with rear cable entry tend to screw together sideways instead.) The fact that chained extensions include multiple redundant fuses, which makes the system unusable in industries such as stage lighting.
Regarding UK wall-warts, what annoys me far more than cable routing is the crappy plastic earth pins that many of them have. I cannot understand why these are allowed. I have actually witnessed one snap off and stay in the socket when the plug was removed, thereby leaving the socket disabled and with its shutters open.