Unless the government (the people) buys it and funds it through taxes, it doesn't seem to be anywhere near the concept of a public square, just like a newspaper isn't a public square, and the commercial TV and Radio isn't a public square either. Neither are phones. Or billboards.
If something becomes ubiquitous enough to be regarded a public square, we either have to make it one, or fix the reason why a commercial for-profit company is regarded as public square in the first place.