Not at all, most people do not take different pictures of the same scene under the same settings from about half a dozen flagship phones, post it on Instagram and ask which one is better. In fact, this is the only time I've seen such usage.
In practice, people use a single phone to capture moments that do not come back and even if the scene is repeatable people prefer to succeed on the first take, therefore they will take photos until they get one that is good enough and editable. Most people don't even know how the photo will look like until they try a few edits. It is an intuitive process that involves multiple trials and misses.
So the best camera is the one that gives you the photo that is easiest to edit to achieve the picture you desire. #nofilter is a special case, a niche and If you ask me, it's not a nofilter just because the device applied a filter by itself.
Anyway, if that test was correct the cheap and great photos phone would have been a viral hit. When people see a great photo, they do ask how you took it. That did not happen.
If you want perfection, get a proper camera and more importantly learn how to shoot with it
This test for real-life camera usage is as objective as it can get. Most people shoot pictures to put on social networks, not to submit for documentary film awards.