All sorts of ways to quantify "better". In no particular order nor an exhaustive list:
• Superior sharpness, contrast, flare resistance, CA, coma, distortion, vignetting, bokeh, etc.
• Faster and/or more quiet AF
• Wider aperture
• Smaller and/or lighter
• Less focus breathing
• Better build (e.g. more weather resistant)
• Internal Zoom
Of course, these "better" qualities may be at odds with each other. The most obvious example would be "smaller and/or lighter" and "wider aperture", such as a 70-200 / 4 vs a 70-200 / 2.8. The former is smaller and lighter whereas the latter is a stop faster. Many may well prefer the lighter weight and smaller size over the extra stop even if the prices for the two lenses were the same.
As for your third paragraph, well, that's outside my experience. I don't know what you mean by "only one [lens] that works for a given situation". That's like saying that there's only one car that works for a given situation. Sure, I wouldn't take an Audi A8 off-roading, but there are plenty of outstanding cars for performance driving and for off-roading. And while I may have a favorite car for any given situation, any number of cars will get the job done more than satisfactorily. Likewise, the same is true for cameras and lenses. More than that, it's easy to see that even if I did have a favorite car for a particular task or tasks, that another car might be made which I would like even better for the same tasks, which is true for cameras and lenses as well.
The bottom line for me is that, with the exception of very specific needs, any and all modern cameras and lenses (and many not-so-modern cameras and lenses) are well, well, well past the "good enough" point for the vast majority of people and situations. By "good enough", I mean that you did not miss the shot with what you had but would have gotten it with better equipment, and that the shot you got would not have been more likely to sell (or sell more copies), gotten more likes, or placed you higher in a photo competition. Now, of course that is simply not true for every situation -- there are definitely shots that better equipment will get you that less equipment will not, and there are definitely venues where better equipment will increase the chance/number of sales, get you more likes, and/or place you higher in a photo competition. But for the vast majority of people in the vast majority of circumstances, it is my opinion that it will not.
So, if my opinion (that modern equipment is well beyond the "good enough" point for the vast majority) can be taken as true, then what's the point of "better" equipment? To expand the range of your photography. With better equipment, you may attempt photos that you used to never attempt, you may print/display photos larger, you may take photos in a greater range of light, you may process your photos more aggressively, etc., etc., etc.. Or, you might not, in which case, "better" equipment serves no purpose for you.