Not always.
For us rural dwellers the power just normally comes out of the substations as a single 7200 volt feed and go for miles, some times 20 -30 miles, with a simple two conductor single phase or four conductor 3 phase overhead or underground line set out to the many homes and end users.
If the voltage drop is bad enough at the substation they will change taps to raise the output voltage there but still everyone is basically on what comes down to being just a really really long extension cord and how stable your line voltage is is directly proportional to where you are and how much load there is at any moment.
I for one am close to a new and rather large primary three phase feeder line that is double fed now from two substations so my voltage is generally quite stable regardless of how much power I draw even during occasional bursts into the 40+ KW range when my big shop equipment starts up while other high draw devices are running.
However if I tried running my same loads at a buddies place who is at the far end of a long single phase feed put in back in the 1950's there would probably be severe voltage dip issues large enough to affect numerous neighbors up to a few miles away from his place.
That's still no excuse
If a feed is too small (and a 1950's feed could well be far too small by now) then it needs upgrading. If it's going 20-30 miles it would obviously benefit from a higher voltage line.
There was a situation in Matlock (where I work) where a
LOT more houses were built at the end of a road with an underground feed (as most UK wiring is underground) - this caused low mains supply problems, because it was never designed to carry that load. The solution, fairly obviously, was to dig the road up and run more suitably rated cabling.
The company I work for closed one of our shops a couple of years ago (it wasn't doing much business, as it's in a mostly tourist town), and we now rent it out. Behind the shop (the other side of a car park) was the service department, and this has been converted in to two apartments (there's also two big wooden garages - these are planned to be knocked down and a further apartment built - if/when planning permission can be obtained). The workshop obviously only had a single mains feed, and a single meter, so we asked for a second meter to be fitted - to be told that for this to be done we would have to pay to have the underground cable replaced as it's not large enough to feed two meters. As this would cost about £20,000, and cause utter chaos (as it would prevent access to the car park and the other businesses around).
So in the meantime both apartments are fed from a single meter, and the owners pay the electricity bills - with the rent on the apartments adjusted accordingly.
Bit of a bodge, but it works for now
Presumably, if the further build goes ahead we would have to have the supply replaced - but as it stands there's no low voltage problems at all, just an electricity board requirement to meet modern standards rather than the standards when it was installed.