I don't understand why city centers would be outcompeted, and this sort of legislation seems rather heavy-handed not just from an American perspective. In the country I live in, the same grocery chains have mostly smaller (with some larger) stores in urban centers and mostly larger (but less frequent) stores outside these areas. I can get most common items at any of the stores near me, and if looking for a less common item I can go to a larger store in my city which will almost always have it. This means that I'm connected by public transit to both small and large stores, neither of which need cars or massive parking lots.

Well, it largely succeeded in preventing shops moving out from city centres in NL, and can be presumed to have encouraged bike usage over car usage, as inner city shops are more likely to be reachable by bike.