"That said, though, the worst CF in this scenario is getting away with it completely unblamed. I actually think that OP should consider contacting the care agency/council, but in a positive way. This man is doing an essential job, but is neither provided with the time nor the facilities to do it properly. If they can't ensure that he has somewhere close to the client to park (maybe having to carry in bulky supplies/food/medical equipment) - even having got him a parking permit on an oversubscribed road - the onus should be on them to pay him for the extra time it takes him to park as close as possible in an available, appropriate space and then go to the client's house. I believe Royal Mail take this into account, by giving a much shorter round and transport if necessary to their workers delivering to remote houses and those with very long drives, so goodness knows how a care agency is allowed to just blatantly ignore this need."
Although I'm not sure I agree with calling the man's employer, I DO agree that this is an option that should be looked at from the employer point of view.
I have a friend who works for a council social care department (I doubt it's called that, but it's still where she works) and her job is managing the carers who are sent out to people in need. For the last few years, her job has been to pare the services to the bone and maximise the number of visits in a day, to get "value for money" from the care workers. Allowance for travelling time is at a minimum, and as for finding parking, I doubt that's ever factored in. Given that the number of cars on the road is so much higher, and therefore more people needing parking spaces, it would make sense for these employers (council or private) to have access to parking permits that DO allow employees to park ON THE ROAD (NOT on other people's driveways) in places that are restricted. Of course, they would still have to park safely, but for e.g. they'd be able to use Permit holder spaces, paid parking spaces etc. without penalty.
It wouldn't be the total solution but I also like the suggestion of having a pre-printed placard in the car, explaining why they've parked where they've parked - and including their phone number - because if you DO "have to" park like a twat, at least make it easy for people to call you and ask you to move.