I've always worn watches, and I'm used to being able to see the time when the face is angled away from me—anything short of 90°. It's something you take for granted with an analog or always-on digital watch, and if you're used to it, having to arc your arm to wake the screen is a palpable annoyance.
Like many things, it is a far bigger issue in the imagination than it is in reality.
I bought an AW2 having spent years wearing Garmin sports watches on a daily basis, and other watches before that. As you describe, I was quite used to being able to glance at my watch to see the time without making any movement. I too was concerned about the screen being off except when activated by movement or tap or crown. Seemed like it'd be annoying.
The reality, as it turned out, was that it's not nearly the big deal I'd imagined it to be. Go figure.
So yeah, if you focus on that single aspect it can seem like it'd be a real annoyance. For me it really hasn't been. The many advantages / capabilities of the watch so far outweigh that downside that it'd have been silly for me to have let that keep me from buying one.