I don’t think having the only running vehicle on streets full of stalled and occupied vehicles is a prudent tactic.
There would soon be a high body count of competing car jackers...yours among them.
Did you read the book, One Second After? The protagonist’s mother in law had an older car with no electronics and they were able to drive around unmolested and there was a hippie clan in the woods with older VW’s and no one raided them.
But I do wonder about a real life situation as you described.