The 6P has quick launch as well, and it's just as fast if not faster than the S6 (I use an S6 side by side with the 6P and have done extensive testing). Some review sites commented it was even quicker as well.
The S6 app has a few more features, but there is nothing really lacking from the stock google app except a manual or "pro" mode. Stills, selfie cam, slo-mo, video, etc. is all intuitive and easily accessable. Pano mode is better on the S6. Apps like Pro Shot or Manual Camera unlock more features for both.
The tiny sensors used in these cameras ensure that pretty much everything is in focus all the time, even at F1.9 (GS6) and F2.0 (6P). The selective focus/ lens blur is just a software effect, and other apps can do that, as can computer software. As someone used to "real" background blur on actual full-frame cameras, I find the simulated effect ugly (purely subjective of course). Usually when you're using your phone as a camera, you want more things in focus. F2.0 on these little sensors is roughly equivalent to around F11 (from a depth of field perspective, not a light gathering perspective) on a full-frame camera to give you an idea of why everything is always in decent focus with tiny sensors.
HDR+ is unquestionably better on the 6P for low-light. It simply takes better low light shots. The S6 does the HDR faster (instantly), but it is more for high contrast scenes rather than low light. The 6P is definitely better in low light, and it hangs on to color accuracy longer at the higher ISOs with less noise. Outdoors in bright light, the S6 gets the edge in resolution only, the quality of the image capture is the same on both cameras. The S6 has a few other tricks such as tracking autofocus which can be helpful for all the parents trying to keep up with their kids. Optical stabilization is a plus on the S6, but it mostly helps for video capture. The videos I took handheld with the 6P were plenty stable as well, but I give the edge to the optical stabilization still.
I agree some of the things you say but I do not agree that it is a "distant" second. I would say they are equal, because they have different strengths, and overall they are both objectively the best cameras on any smartphone at the moment. DXO labs doesn't think it's a distant second either.
The S6 battery life is actually pretty decent (on my copy anyway). The 6P's is flat out incredible though so the S6 doesn't even come close in that department. The Note is a better comparison for battery life.