I live abroad and pavement parking is illegal, as is parking on the wrong side of the road (facing the opposite way to the direction of traffic). It works very well indeed here, but we don't have the incredibly narrow roads you find in so many parts of the UK. I remember living in England 200 meters from a small commuter train station on a cul-de-sac of semis which all had drives and garages, and everything was great until the station carpark was made pay and display. Overnight it became a far less pleasant place to live with small children and babies because the pavements on both sides of the road were parked on meaning there wasn't room for even a single buggy, and it wasn't possible to cross with a clear view because there was no choice but to park between parked cars. Really shitty. The newly pay and display car park was virtually empty every day.
Pavement parking is really shit - it seriously impacts on quality of life for local residents. It's so much pleasanter to live somewhere it doesn't happen.
However going back to the UK it's sometimes startling just how narrow roads are compared to a lot of European countries (with the exception of mountainous areas). The roads really aren't fit for a population who expect virtually every adult to have their own car. At all.
It's also massively dangerous for children in many parts of the UK especially England to walk to school because of pavement parking and far too many cars on the road, which is a vicious circle and a really bad thing on multiple levels.
What's actually needed, given there isn't space to widen the roads, is very drastic measures to improve public transport beyond all recognition and seriously disincentivise private car ownership.
That'll never happen obviously. People only vote for their own short term personal interests so no political party would try to bring in anything sweeping enough to actually improve things because short term it would be unpopular.