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Depends on how you define necessary.
Perhaps if we work through an example that might be useful. My colleague is a duty social worker and number of times throughout the year will be called out during the night to attend a domestic situation where there is concern for the safety of a child. Even if the location of the call out were on a public transport route, at the time of night, the services simply aren't running. Due to the sensitive nature of the work, use of a taxi service isn't appropriate and given that there may be a need to transport vulnerable children neither is a bicycle.
What do you feel makes the ownership of a private vehicle and use in these circumstances immoral?
Neither a right nor a privilege. Simply immoral in towns where for most it isn't necessary. Exemption for some people who should be allowed a mobility vehicle on prescription.