At the end of the day it is not a dream home if it doesn’t work because you can’t park conveniently.
I think every house will have a compromise somewhere, you have decide what compromise you can cope with. I don’t think this sounds like a compromise that would work in the long run.
Also, where would visitors park?
If it is private, do you become a part owner when you buy the property or would you merely have right of access?
If you become a part owner, what is set up with regard to maintaining it? Is there a sinking fund taking in annual contributions so that it can be repaired or will it fall on those who live there at the time to pay for repairs regardless of how long they have lived there or whether other owners have lived there, used it and moved on without ever contributing.
Might not be an issue or it could be in the future…