FWIW, I think there are differences between laws that regulate federal property (e.g. post offices, federal parks, military bases, etc.) and laws that regulate either public (streets, sidewalks) or private (any business, non-gov organization, or residence) property.
The owner of private property absolutely does "allow" someone to carry (or prohibits them from carrying) a weapon onto their premises. If a restaurant, or retail store, or any other business welcomes firearms onto their property, they are indeed "allowing" them. It is their right, as it is their property.
The difference in this case, of course, is that the owner of the property is the federal government. So we're not talking about private property, and therefore circumstances are a bit different.
If I was making a proposal for an all-encompassing federal law, I would borrow from the "Kansas plan" and extend it ... something like this:
The management of any federal government property that chooses to prohibit visitors from carrying weapons on its property must:
(1) provide sufficient justification as to why persons may not carry weapons;
(2) provide sufficient security to protect all persons on the property at all times; and,
(3) provide a secure location for weapons carriers to store their weapons near the entrance of the property.
Any property that meets one of the following conditions may not prohibit the carrying of weapons:
(1) any property for which the management cannot reasonably control entry and exit, such as a park, forest, wilderness area, etc.
(2) any property that is commonly used by many members of the public, such as a post office, social security office, veterans affairs office, museum, etc.
There could be minor exceptions carved out - e.g. areas that are used for hunting could prohibit rifles and shotguns during non-hunting season - but I think this would cover most circumstances.