It's very much a solved-many-times-over problem. Search the following terms: bike child seat, extracycle, bakfiets, Burley, kid bike tag along. Those will take you all the way from infancy to big enough to ride their own bike. You wouldn't need all of those, but you could probably buy one of each for a total cost of less than 1/4 the cost of one car.

Your baby entitles you to drive, thereby endangering and impoverishing everyone around you? Yeah you're right, there's an out-of-control sense of selfish entitlement in America.