Show me the line that says it has to have such a line.
Article the eleventh .... The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people.
Article the twelfth ... The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people.” (https://en.wikisource.org/wiki/United_States_Bill_of_Rights)
Further, show me the line of the constitution that specifies the technology by which any of its rights are to be executed.
Show me the line that says it has to have such a line.
If I want to fly and apply myself fulltime, I can have my flying license in a month, being free to roam most of the national airspace (as long as I tell some people where I'm going, so they can help me prevent collisions).
I would surely expect it to be the same in the US: everyone has the right to travel by air, provided they adhere to a minimal set of guidelines to prevent them from endangering themselves or others in ways obviously directly related to the 'flying' itself (and not to e.g. the suspicion that someone might have a 1% higher change of using the plane for a terrorist attach).
http://www.un.org/en/documents/udhr/, article 13.1: "Everyone has the right to freedom of movement and residence within the borders of each state."
"and the government can set whatever standards they want for public spaces"
So, in your opinion, a government can decree that whites can't travel first class in planes, or that women must wear a burkha on the street?
For me, all that hyperbole makes it hard to see what value your arguments have.