Also, in most cases, the switch is only across (the wire that is supposed to be) the hot lead-- with neutral and hot swapped at the plug, you're not only energizing the outer ring of the light bulb socket, but also leaving it energized when the switch is off.
This leaves a shock hazard exposed even when the switch is off-- the lamp still won't light under normal circumstances because there's no path to ground with the switch off on the neutral line, but if you provide it one (your body) by touching it, you'll still get a shock regardless of the state of the switch.
Yeah, comment kinda got downvoted into oblivion for a slightly off example, but this was kind of my point. There are a lot of appliances that become significantly less safe when you put the power into places it's not supposed to be. And the danger is non-obvious.
oops, yes, good point.
Another commenter pointed this out, but I have to chime in as well: no. Not true. The neutral is NOT bonded to the exterior body of a metal lamp. Not even on old fixtures built in the 1960s.
The old fixtures, if they were metal, were often not grounded, i.e. the lamp might not be connected by a 3-prong plug (hot, neutral, ground). But the neutral was definitely not bonded to the metal body.
If you inspect a new fixture, typically this means: it is either constructed with no accessible conductive parts, OR its metal case is bonded to the ground (not neutral!) and it has a 3-prong plug, OR it has a step-down transformer that converts to lower voltage before it enters the conductive lamp.
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The thing that does happen when switching the neutral wire on a lamp is that doing so will energize the more-accessible "outer ring" of the Edison female receptacle rather than the less-accessible "center pin". This means that if you change the bulb with the switch on, you'd be more likely to contact the hot "outer ring".