That's a pretty loaded question.
How ethical is it to travel?
How ethical is it to own a smartphone?
How ethical is to buy milk?
If the alternative is Ubering everywhere, you may just be creating “overhead” carbon in the form of the “to and from your location” trips the car will make.
EV and PHEV options are much more easily available now. Chevy Bolts can be had for a song.
If you're really asking about ethics and not morality, then the question boils down to 'what does the society find acceptable'?
Which is to say that, while many complaints about your owning a car you don't necessarily need can be conjured, few that I know of are valuable.
It's more important to be true to what is right than it is to conform, anyway.
Ethics is dependent on the context of what system or culture you are asking about. For example, medical or legal ethics, the ethics of modern American software developers living in an urban area in the US. Or London? So you can't say whether it's ethical or not without that context. It's the rules, laws, and even generally accepted behavior of that society, culture, or organization that tells you what is ethical.
Having morals might actually be about the only thing unethical for a lawyer.
If you were Amish, it would definitely be unethical to own a car even if you needed it for some good reason.
I can't think of too many other situations where simply owning a car would be outright unethical - generally and widely frowned upon, illegal, or against norms or rules.
Moral? that's up to you.