Public proposals are, in another poster's words, really icky, and if anyone did that to me, I'd know they had no idea what kind of things I value and would refuse.
I also find them incredibly manipulative, even at the best of times. Does anyone remember the YouTube video posted on Hell's Belles a few months back with the public proposal that turned into a whole over-the-top wedding? The bride went from sobbing because her boyfriend had been violently confronted by what she thought was either a stranger or a secret girlfriend, to, in front of cameras and a shopping mall of strangers, being asked to marry him right then and there. The whole thing smacked of a smug "Now look at this big wedding I gave her! She can't ever be mad at me for anything." The bride was put on the spot in humiliating public ways multiple times, and had no choice in any of it.
Another example I have is a coworker who had been dating her boyfriend for about six months. He kept wanting to speed things up, and talked a lot about how he wanted to get married and have kids asap. She was barely 22, and kept putting the breaks on, and was even starting to think she should break up with him. The holidays were coming up, so she decided to wait until after that and then have the "slow down or I'm out" talk with him. He knew this full well. What did he do? On Christmas Eve, at his family's house, in front of twenty people, he made a huge production of giving her her present: an engagement ring, and he proposed to her. She refused, and left immediately. A day or so later, during their break-up argument, when she demanded to know why he would do that to her when he knew full well she wasn't ready to get married, he said "But I thought if I did it like that you wouldn't say no to me in front of my own parents!"
So I agree with people who have said, as long as marriage has been discussed between the couple, I'd grudgingly say that a public proposal is okay for them although it still seems more about performance and even control than real feelings.