I agree with your classification
(you can add "high quantity of sulfites" to low-quality. Those taste like the headache you’re going to get on the next day.)
Also while price doesn’t predict which category you are, it’s hard to find a very cheap good wine. You have to either know your stuff, or buy something more expensive
bad - wine that actually has gone bad (skunked, turned to vinegar or some other faul)
low-quality - jug wine (high sugar and/or extremely high acidity and/or strong ethanol flavor)
average/meh - the wine is drinkable and nothing stands out
good wine - the wine hits all the key traits of its varietal
Those super-sensitive can get more fine grained, and anyone who doesn't hate wine will have a 5th "great" category based on their personal preferences. But those are replicable consistently across the population.
The average/good distinction is trainable for the average person with some practice.