What, exactly, is the 'service' that needs to be paid for? Is it the creation of the work in the first place? I have no problem with artists having the right to stop producing works if they're not paid. Or is it the replication of the work? This is not something the artist does, with digital works. And herein lies the problem.
You are looking at things with the assumption that copyright is a natural system, and any deviation from that system requires a justification. Hence your taking as an axiom that allowing others to copy a work is a service provided by the artist for payment.
I feel that a more rational basis is assuming a system of no laws as a 'default' state. Any deviations from this state require a justification of how they would benefit society as a whole.
To give an exaggerated example, let us consider whether murder should be outlawed. In a 'default state', there would be no prohibition on murder, and anyone could murder anyone else for whatever reason they like. It is clear that murder may benefit the person doing the murdering in some cases; is there a sufficient cost to society as a whole? Naturally there is - the fear of being murdered forces everyone to take security precautions into their own hands (inefficient), and causes needless pain and suffering. So murder should be outlawed.
Now, let's look at theft of material goods. Note that theft of physical goods and copyright infringement (or unauthorized copying) are two entirely different things, and must be treated as such - in particular, theft deprives the original owner of enjoyment of the object in question. So, why is theft of material goods a bad thing? Well, in a capitalistic society, material goods are provided as compensation for doing something of benefit for society (ie, payment). Allowing theft subverts this system; those doing the work don't get paid, and instead thieves get the benefit. The nash equilibrium of such a state is for everyone to engage in at least some level of thievery, which competes for their time - thus reducing the amount of useful work performed. Thus, societal efficiency drops, for no benefit on average. As such, it should be outlawed.
What about copyright? As a first-order effect, it's clear it benefits the artists (although this becomes unclear when you consider the additional advertisement provided by free availability of the works in question). However, what about everyone else? On average, does society as a whole benefit from this deviation from the 'default state' of no copyright law? It's clear there's harm to individuals other than the artist - they must pay, or they are prevented from doing things they would otherwise be able to (ie, replicating the work). So there must be a corresponding benefit to others; the benefit gained by the artist cannot alone offset the harm to society as a whole.
The original conception of copyright aimed to increase the prevalence of artistic works, by providing artists with royalties. This was the benefit to society that made the original equation balance. However, with the Internet, there is no shortage of artistic works being provided completely for free by the author, with no copyright royalties coming to the author. This lessens the benefit to society provided by copyright law.
We must also consider the additional costs of copyright law added in the modern era. 'Mash-ups' are artistic works in their own right; however, copyright is used to force them to be removed from public view. This was a scenario that would have been unheard of back when copyright law was first envisioned, and is a further cost on society as a whole.
But, you might ask, isn't the provision of material goods (ie, royalties), the basis for encouraging work for societal benefit, as in the theft example? I would argue that there are a few important differences:
* It has been demonstrated that there is no shortage of people willing to do artistic work for free. This is not the case for all jobs - eg, there are very few people willing to work in a sewer for free.
* It is still possible for artists to be rewarded for their works even without a system of royalties. Donations, commissioned works, advertisements, hard-to-replicate physical goods (special CD cases, etc), and live performances are good examples of this.
* People sometimes choose to pay for something even when they can have it for free. This is irrational behavior, but it's how human psychology works - just look at the humble indie bundles (http://www.humblebundle.com/) as an example. You could buy the bundle for $0.01, or you could even just snag a copy off bittorrent or something (there's no DRM!), but yet the average payment for bundle #4 is $5.33 - and the current total income is at $1,578,109.48. Even though copyright is not being enforced here, money is still being made.
* Most importantly, unauthorized replication does not actually deprive anyone of enjoyment of the work in question. As such, the very act of copying creates some level of cultural value, by exposing the artistic work in question to more people. Theft of material goods creates no value, as any additional enjoyment in the new owner is offset by the deprivation of the old owner of enjoyment of the object in question.
In short, copyright was a good trade-off between individual rights and societal benefit back when it was first conceived. However, things have changed, and it can be argued that copyright no longer provides such a benefit. Once it loses its reason for being, it should be repealed, or modified to bring a net benefit to society. I certainly cannot support anything that would attempt to simply extend copyright at this point.