The first stop is for the crosswalk. (I might do this even when the light is green if there is a pedestrian in the crosswalk since never hitting a pedestrian is a rule of mine.) If I see a pedestrian in or approaching the crosswalk I wait here until they are completely cleared. Then I slowly roll forward for the second stop. This is the stop I use to check for approaching motor traffic. I have better visibility now because there's no longer a lifted F150 blocking my view to the left. Assuming I do notice an approaching vehicle I'm supposed to what? Drive into it? I would love to be in court accused of failing to run a red light into active cross traffic.
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.
I don't really find anything wrong with your approach (I do the double-stop sometimes too, if conditions warrant it). But coming to a complete stop (once or twice), for many intersections, for many road conditions, for many times of day, is not going to meaningfully increase anyone's level of safety (yours, another driver's, a cyclist's, a pedestrian's...) vs. a momentary pretty-much-but-not-really-stopped stop.
To use your phrasing, the risk of anything bad happening after a not-quite stop may be overblown.
Sure, I'll agree that there may be times when the "extra" caution is unwarranted by the situation at the intersection. But by doing this every time I ingrain it as an automatic habit which greatly reduces my ongoing risk of failing to use extra caution at some point where it is warranted!
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.
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.