I did a degree in creative and professional writing after studying engineering/science, and one of the only things I would say that I actually learned in that degree is that one of the things that defines works of 'art', in any discipline, seems to be that it has a different effect and meaning for those experiencing it. Something that resonates for one person doesn't necessarily resonate in the same way for others. It's completely fair to think an author is overrated, or even just particular works, it's part of having your own critical mind and opinion on such things. I don't think anyone actually reading all of the classics really appreciates every single book that could be defined as 'classic' unless they're a huge literary nerd, and even then they'd have to be a very specific type of literary nerd.
Classics are known as classics due to a wide appeal, but none are without critics. That appeal may wane with time, as the issues and perspectives in the books grow less relevant, or the use of language becomes less approachable, but they rarely ever have that classification of 'classic' removed- because after their peak they become a reflection of a time and a place in which is was widely accepted and appreciated.
I think poetry finds itself in the same boat, but the entire genre has a continuously diminishing readership. Arguably songwriters are poets, but the traditional written piece seems to be falling out of style quickly in comparison to its contemporaries, plays and novels. Even at its peak, poetry was never an extremely lucrative field, and very few authors made their living just writing poetry (though I do have a limited historical view of this; I'm a technical writer, not a literary historian!).