Anyway, you can drive however you want. I've been driving like this for over 30 years all across the United States and I have never been pulled over, cited, rear ended, or even, as far as I can recall, honked at while pulling this particular maneuver so I think some of the risks you are imagining may be overblown.
To use your phrasing, the risk of anything bad happening after a not-quite stop may be overblown.
Since the failure mode is an auto accident and the cost of the habit is marginal I feel comfortable promoting this behavior. I have definitely seen accidents and many near misses caused by people who failed to come to a complete stop and look around when conditions did warrant it.
Another lesson I learned in driver's ed is that traffic approaching from the left can be traveling at a speed that completely synchronizes with the A-pillar of your moving vehicle, causing it to be completely invisible to you right up until the moment it collides with your front driver's side fender. This is why I stop and move my head around while I look, to make sure I'm not missing anything. I'm just a stupid human after all.
You are correct that it's not compulsory to turn right on a red, however, if you are going to turn right you can't just stop in the middle of the intersection you either stay back or you go.