I've had one power cut in the last decade (urban area, wiring generally underground), but I know people in rural areas who have power cuts a lot due to storms, and sometimes there are problems coming back up. Think it's mostly old-fashioned 'fuse boxes' with actual literal fuses in them that have problems (you don't strictly need an electrician to sort that, but some people are nervous of the giant fuses and I'm not sure I blame them...)

I don't think it's a particularly _common_ issue, but it definitely happens to some extent.