Modern day cars are much more complex than cars of say, 20 -30 years ago with more to go wrong, and some of those potential mechanical and electrical failures could be very expensive.
An extended warranty won’t be for everyone - it depends how risk averse an individual is. It won’t even be a consideration for some owners; those who lease and those who buy with PCP and hand the car back when it’s three years old. However, for those owners who do buy an extended warranty, it will give peace of mind to some degree against potentially large unforeseen repair costs that might happen and which probably haven’t been budgeted for - e.g. blown turbo, failed DSG transmission, failed infotainment unit.
Some owners will choose not to buy an extended warranty but instead will create a ‘repair fund’ that they periodically add funds to, so if faced with unexpected repairs to their car, they have a fund to draw upon to help pay for repairs. If there aren’t any large unforeseen repairs to pay for, then they’ve got a pot of money to use as the please. Other owners will do nothing.
An extended warranty won’t be for everyone - depends on a number of considerations which will be different for everyone depending on their individual circumstances. Will I buy an extended warranty when my car is three years old? Maybe, but at the moment I’ve not given it any thought as I’ve only just got my current car.