The economic justification is that free markets will not provide enough profit for artists to undertake some projects for which the social benefits of doing so outweigh the costs. Optimal copyrights will compensate artists just enough so that they are willing to create the works, anything above that is inefficient rents* (you hear that Metallica!).
The popular justification seems to be more about maintaining some “fair” balance between consumer surplus and producer surplus. The measure usually being that people who create things that generate a lot of social benefit (e.g. they write hits) deserve to get proportionally rich. Even after the artists are dead people feel that the benefits should flow to his children, wife, estate, etc. in proportion to the social benefits. This, I suspect, is simply the status quo bias. In this country artists who create very popular art have tended to get very rich from it, ergo we have come to see this as the “fair” outcome.
People seem much less concerned that the payment to roadworkers be in proportion to the benefit that society gets from that roads they created, and that the payments continue to flow long past when the work is done. The same is true of the designers of those roads.
Why should we be disproportionately concerned about artists ability to capture economic rents? Why should we be concerned about the ratio of producer to consumer surplus in the arts and not for other workers? Wouldn’t we be better off in a world full of middle class artists but more art?
This, to me, seems like yet another area for liberaltarian agreement.
*For more on this, see Alex Tabarrok’s “Patent Theory versus Patent Law”.