I just look at the RD from behind and judge the angle of the pulley wheels to the cassette. Is that not precise enough?

Only if you have sharp eyes, (and I mean very sharp. Best is to measure, but you don't need to shell out for a $50.00 tool. If the Hanger is square, then the Rd is vertical. Therefore is follows that the lower pulley is directly under the upper pulley, which is centered below the sprocket, who's bottom is centered below the top. That means you can determine precisely whether the hanger is square by measuring as I described in an earlier post here.

I assume you can find a straight edge and small ruler easily enough. A friend would also be handy but you can do the job solo if you don't have one.

Your eyes can deceive you, don't trust them.

I'm pretty sure that a rider this past Sunday had a bent hanger, but I heard it more than I saw it. It was only after I could ride behind him for a couple minutes that I could get a good look. It's still hard for me to tell when a bike is on the floor or in a stand, especially if the RD is bent just enough to add noise or shift funkiness but not so bad that anyone could spot it from across the street.

I'm by no means an expert, but to me, it is fairly easy to see if it is perpendicular to the ground but harder to see if it is parallel to the wheel to wheel axis. There are two planes at work, and one is easier to see. I think I am explaining it poorly, but if your rear wheel is a clock face, easy to align parallel to the 12 to 6 line but much harder (for me at least) to get the 6 to 9. That's how the tool became invaluable to me.