The worry that motivates parking minimums is, if your street has 1 parking spot per home, and my street has 0.5 parking spots per home, that car owners will buy homes on my street anyway, and they'll park on your street when there's no space on mine.
This is called 'displaced parking' and it's a pretty well known problem among parking planners. You'll get the same thing if, for example, the college campus starts charging $5 to park when students can park for free on nearby streets and walk.
You can get around this with parking permits and towing everywhere in walking distance - but you can't be timid and imagine the new street won't interact with other parking locally.