"Is the strap button's purpose just to hide the long screw head?"
Yes, pretty much.
A high break angle is not as important as many seem to feel. In an experiment I did using a mechanical plucker, which pulled the string straight up, six degrees of break angle was (barely) enough. In most real playing the string does have some sideways displacement, which would cause it to roll on the saddle top, so a bit more break is required. Still, as far as I can tell, 12-15 degrees is enough.
The higher the break angle is, the more force there is trying to tip the saddle forward. This can break out the front of the slot, which is a very difficult thing to fix well, short of replacing the bridge.