(Also, the kind of rolling stop I'm talking about isn't a 5mph roll, it's a near-stop that feels like a stop to the driver but technically doesn't actually bring the tires to stationary. Odds are even you have done this kind of stop pretty regularly without realizing it, and even a cop wouldn't even notice it as incorrect unless they were actively looking for someone to ticket.)
The second stop may actually be illegal in its own right depending on the state.
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.
Because people don't. That's just a fact of life, and we even have silly names (like "California stop") for the all-too-common behavior of barely or not completely stopping at a stop sign before continuing on.
I'm not excusing this behavior (even though I do it myself), but it's a widespread fact of life. The world is squishy, and I don't think it's reasonable to punish everyone for not coming to a full stop every single time, even if it's 0.01% safer to do so.
It's also kinda hard to define a "full stop". Well, obviously there are some states that are very obviously a car at rest. But if you were to, say, graph my car's speed at an intersection with a stop sign, you might see a curve that flattens out to where the slope is zero. Maybe that zero-slope point is a teeny tiny fraction of a second, though. Did I come to a full stop? Yes! Can a cop actually realize I did come to a full stop? Often not. Ok, so I did stop, but did I give enough time while at a full stop in order to assess that it was safe to continue moving? Do I even need to do that after I've come to a full stop, or can I start that assessment when my speed is 3mph, and know by the time I've fully stopped that it's immediately safe to continue? I think so, yes.
It's just fuzzy. Humans are fuzzy. The law is fuzzy. Safety is not a yes/no binary, it's fuzzy. Many many people don't always come to a full stop. That's just a fact; asking why is probably pointless.