It's hardly a matter of belief: we're pretty sure of what the limits of human hearing are (and that can easily be tested) so if two devices are performing well above what we'd be able to discern in their performance you won't notice a difference.
If this was not the case it would be in the best interest of any of the manufacturers of expensive equipment to setup a credible A/B test that would show how a difference can actually be discerned. But they won't, because it can't.
You can leave it on (or Dolby Atmos if you buy it) and it won’t make a difference for stereo sound. It’s only supposed to make a difference for 5.1 or 7.1 audio where it’ll simulate speakers around you. It’s great for shows or movies with surround if you only have stereo speakers. For games you may be better off using the headphones mode of the game when it has one and leaving that off.
You shouldn’t need an app for just pairing and using them with out-of-the-box settings but any EQ settings or other features beyond the Bluetooth standard need an app because none of it is standardized and that’s unlikely to change.
If you got a dud send them back, no point trying to “fix” it.