I wouldn't say navigating by bezel wouldn't be functionally possible with a square screen, it would just work differently. Indeed, an actual rotating bezel would not be first choice, but a touch sensitive one in which I could slide my finger around to access functions would be cool. That same technology would also work on the square shape, and would be far more preferable to the Digital Crown. I actually think the DC is the most blatant fashion concession and pointless feature of the watch. It looks cool, but it's not easy to use, and it presents a major point for mechanical breakdown, as evidenced by the reports of washers coming out, and the need to rinse it out under running water. It also works differently for left handed users.
If Apple delivers on the rumor to significantly increase the screen size of the watch, then any current screen real estate advantages offered by a round watch over the square will be rendered moot. The AW will likely actually gain display space, which is great for those who like to read extensively on the watch: complete emails, lengthy text conversations, news articles, contracts and legal docs, etc. And, for those who like to cram as much information on a watch face as possible. But for those who use the watch as Jony Ive intended -- for quick glances -- then either shape will serve the function well. I don't know about you, but I never walked around staring at my wrist watch in the past, and I don't intend to start doing so now, or in the future. The fact that technology allows the watch to display lots of text, doesn't mean it's the proper tool for doing it.