No, there really isn't any significant simplification possible. When you interface to the power line, you have to make your design as robust and fail-safe as possible, in order to avoid product liability issues.
Even if the design of the wall socket permits only one physical orientation, there are enough mis-wired wall sockets out there that you really need to treat both Line and Neutral as "hot" inside your product.
A couple of things.
A very small point, the UK is in Europe, and AFAICR we have had 3-pin plugs, 3-wire cables, since the late 50's.
My house was rewired in the 80's, and we have Earth Leakage Circuit Breakers (ELCB) on every circuit. So even if I stuck a fork into my toaster while grabbing a copper water pipe, I'd expect it to trip (I am not willing to back this up with evidence :-)
When I have visited continental Europe, I am pretty sure that I've seen the same ELCB technology in use.
I suggest that is even more effective than having an Earth connection; after all, if I touched the correct bit of wire in your toaster with my fork, without touching anything else, the Earth connection via a plug would do me no good. Further, unless the device had a metal case connected to Earth, I don't think I am much more likely to touch both Earth and live than just live alone.
I imagine the cost of rewiring all of the houses in Europe which have two-wire cabling t have three-wire would be very large. However, upgrading the distribution panel with ELCB is pretty simple (a drop in replacement in some cases for an old fashioned fused unit), and could be caused to happen more easily when electricity metres need replacing.
Best Answer
The wide slot is supposed to be the neutral, the narrow slot the hot.
Neutral is nominally supposed to be near ground potential. However, there's no guarantee the receptacle was wired up correctly.
If it is wired correctly, and if a correctly wired polarized plug is used, then the threads on something like an Edison-base light bulb will be near ground potential and there is less chance of an electrical shock than if the screw is at 120VAC with respect to ground. So, it's 'safer'.
It's also backward-compatible with older non-polarized plugs that have two narrow blades, however newer plugs that are polarized are not compatible with older receptacles (barring the improper use of tin snips).
Edit: As kabZX points out, when one side of the line is switched or (most importantly) when one is fused, it should be the hot side only.