How very narrow minded. Are you really that deluded, or just very dismissive.
Just tell the disabled mobility scooter/wheelchair user to park it 3 streets down
Tell the nurse coming as a carer to the lady at number 5 to park 3 streets down (the extra time won't impact her later visits all that much, she can just make it up by skimping on Mrs Jones visit later or working late)
Tell the guy at number 17 to not have that heart attack today, the ambulance can't get through
Or Mr Barrow should tell the funeral director to organise the funeral of his wife for a different day as the hearse wont be able to come to the door.
Mrs Jenkins, no chemotherapy today!
Tell the builder coming to do yokr kitchen extension to park 3 streets down and heave his kit all the way (or take the day off, who needs to work anyhow? no one needa money)
Many reasons why people need unfetered access to their homes.
OP Included in their post and said there was no way out of their road on foot or via car, yet you mansplain that there simply must be, and suggest some stupid reason they should just get on with it because its saving the NHS money!, the people running usually aren't the most costly to the NHS, and if one of them goes on to develop cancer, or some other non obese related issue then their savings are immediately cancelled out.
OP I'd suggest a complaint to the local council, your MP, the department that hands out the permits for these events, nothing changes (even if it is including your road in the plans for a warden). Good luck.