Since the 1991 death of fun pop music, you'd think that new artists, unable to make quality songs of their own, would at least be able to make enjoyable covers of ones from a better era. Yet even recording a great cover song is hard -- just ask any 13 year-old kid with a guitar who mostly plays other people's songs. It's not just a matter of skill, since some of the originals do not showcase a virtuoso performance. It's more a matter of getting into the right state of mind and being able to channel the original in your interpretation. When the current zeitgeist clashes too much with the one in which the original was written, it is nearly impossible for the new artist to get it right.
How can we see this? An objective way is to look at the chart-topping songs of some year and see whether they are covers or not. Sticking just to the Billboard charts, 1987 saw quite a few cover songs that were good enough to make it to #1, whereas no covers in 2005 were that good. (I chose those years because 1987 is a local peak before the 1991 shift to bad music, and 2005 is a local peak after the shift.) The fraction of all chart-topping songs that are covers is always going to be low, sometimes 0, but this way points us to where those minority of great cover songs are.
Here is a subjective list of 50 great cover songs from The Telegraph, and the truly good ones are almost entirely from the late '50s through 1990 period. In Wikipedia's entry on cover songs, again notice the attention given to ones from that period, and how little focus is given to covers from roughly the past two decades.
Good cover songs don't benefit from being close to the originals in time or style. Some like Elvis' "Blue Suede Shoes" or The Byrds' "Mr. Tambourine Man" were released shortly after the originals and are fairly similar stylistically. But plenty of others like Tiffany's "I Think We're Alone Now" or Soft Cell's "Tainted Love" were released 15 to 20 years after the originals and belong to different genres. What they share is a wild and fun-loving cultural and social environment, which has effects on both the supply and demand sides: the music-makers can easily step into the mindset of one another, and the audiences will have similar tastes from a bird's-eye-view. When the zeitgeist is ruled by self-conscious killjoys, artists will find it impossible to enter into the mind of some other good songwriter, and the audiences wouldn't want such a product anyway -- that would be too retro.
This shows how little the quality of music means to most consumers. They would rather listen to newer garbage than older hits. During fun-music times, there is no trade-off between originality and quality, but in boring-music times there is. If quality mattered more, the pop music industry would be like that for classical music. Rather, all you hear on the radio, in clubs, in Starbucks, on TV, and what gets downloaded on iTunes is new garbage. (In addition to mopey and sappy stuff from the '90s and 2000s, Starbucks also plays music from the boring period after the Roaring Twenties but before the late '50s. They are exact in their aim to avoid playing exciting music.) You're lucky if the dance club plays the originals of "Blue Monday" or "Personal Jesus" rather than the sleep-inducing covers by Orgy and Marilyn Manson.
It's not an original insight to point out that most people in modern societies use music as an tribal membership badge, however it looks like this is not just a function of music but the primary function for most people. If an item has already been used widely as a membership badge by some other tribe, and if people today are generally aware of its has-already-been-used status, then it will not be special and unique to a current tribe. That's why they draw their membership badges from current movies, TV shows, songs, etc. -- no other tribe has already used them.
In safe and boring times, tribal turf wars are more frequent and petty, unlike during wild and dangerous times when people set aside some of their differences to stand up to a larger common threat. (We can use the homicide rate to measure how safe vs. dangerous an environment is.) When tribalism increases, it's even more useful for them to use bad cultural products as their membership badges -- anyone who's not very committed to the tribe can enjoy good culture, but only those who are serious will pay the high cost of listening to Fall Out Boy and watching Family Guy.
These dynamics are what keep most cultural products from constantly improving in quality as market competition and specialization proceed, as opposed to things like batteries or light bulbs that people don't use to signal tribal membership; there prices fall and quality improves steadily over time. Of course, as more and more things begin to fall under the list of junk that people use to "say something about their personality and lifestyle" -- really what tribe they belong to -- the gains in our standard of living will stall out or even reverse, as with our deteriorating health that has accompanied the gradual shift about 30 years ago to a diet that is mostly vegetarian. It is now low-status, backward, and not respectable to eat the mostly animal-based diet that homo sapiens is adapted to.
Economists are right to say that more competition and specialization tends to lead to things of greater value to consumers, but that neglects these increasingly large domains where what's of value to consumers is not objective-although-fuzzy quality but rather tribal affiliation.