I think if you can answer some questions about going car free, you can decide whether it's right for you.
-How would you handle large-item groceries, especially if you have a kid down the line? Things like 48 rolls of toilet paper, diapers, whatever.
-How would you handle medical emergencies?
-Do you need to deal with adverse weather? Would not having a vehicle keep you indoors all winter?
-Do you go on outdoor adventures? Would not having a car prevent you from doing that?
Would it be worth doing a trial run without a car for a year while you save up for one to see how you would manage it? You could use it as a dual selling point for your wife. If you use the time to save up for a new car, you can tell your wife that if after a year you find you need a car after being car free, you'll get a car. If you do fine without a car, you've proven to her and yourself that you don't need it.
If she needs a status symbol, she can figure out how to buy it for herself, and she can really decide how much that status symbol is really worth to her.
You could look at a quality used car instead of a brand new one.