Disagree. Cozy games have falsifiable metrics, they're just not shared mechanics.
Cozy games have some or all of these traits:
- low stakes plots. If the PC fucks off into the woods, the worst that will happen is someone else will lose their job at the Christmas cookie store or the charming small town will have a chain store opened in their picturesque town square
- are forgiving towards failure. It's almost impossible to reach a bad end in a cozy game, and most challenges and opportunities will reoccur.
- require very little dexterity or fast reflexes. At most, you may be locked out of the fishing mini-game if your reaction time is bad
- if they have combat, opponents are monsters and interchangeable entities, or occasionally, occurs within a context that confirms no one is seriously hurt. If you can talk to a character, you can't hurt them, and vice versa.
- death and serious harm is excluded, often to unrealistic extent. Sick characters never die, farm animals are never slaughtered, characters who are in precarious situations will never actually lose their homes/commit suicide/lose custody of their kid/etc.
- have defined end goals but allow for extended play after reaching those goals. A cozy game can be played for as long as you like.
- have a focus on building relationships with characters, but can be played without. Content will be locked behind relationship milestones, such as gear, recipes, special zones; but the majority of the game will be playable without those relationships.
- feature customization and upgrading of a base, whether a coffee shop, a farm, a caravan, or even an entire town.
- are (subjective judgement) cute. There are no hi-rez monsters or gore, characters are charming but not overtly sexualized, environments are pretty
- suitable for all ages, or suitable for a wide range of ages. An 8 year old will get different things out of the game than 34 year old, but both can play.