Yeah... that scenario has been the bane of my existence for a bit now. My wife takes a bunch of pics of the kids in not-so-ideal lighting and every phone that doesn't carry with it a Google seal... well, they are usually absolute trash. She is currently using my trusty old Nexus 6P because it can get the job done where a list of other phones fell on their faces... G4, S7, S7 Edge, G6, V30... every single one couldn't handle it because of HOW they attempt to take the pic.
The problem with those cameras is that in lower light situations, they lean on longer exposures to get enough light. Now, this is fine if you are taking a picture of a building.. but if you have a 7 year old that has a motor that runs at full throttle 24/7, yeah, longer exposures ain't going to cut it.
HDR+? Well, it goes about things differently. Rather than take longer exposures, it takes MORE (shorter) exposures. Then it goes in and snags the best picture in the set (presumably the one with the least amount of blurring) and builds the final image off that one using data from to others to clean things up. Brilliant system.