To play devil's advocate to the "private platform" argument: we force tv networks and radio stations to give equal air time to all presidential candidates.[1] NBC is a private a company but if they permit one candidate to host SNL they must give the other candidate(s) an equivalent opportunity so as not to unfairly sway public opinion. I don't necessarily think that "infringes" on NBC's right to run their platform as they want. They're still given the option of whether or not they want to wade into politics on their airways but once they do they're obligated to open their platform to both sides.

Now you could argue that Donald Trump expertly exploited exceptions to the "equal-time rule" in order to get much more coverage than his competition, but that's more to do with the structure of the law than the spirit of what it's trying to accomplish.

[1] https://en.wikipedia.org/wiki/Equal-time_rule