That's an interesting legal theory there but it brings up a critical question: If I create something of value to others, do I own it? Should I be able to sell it to others? To what extent should I be able to control its distribution?
The US has a reasonably good body of law regarding this issue, it's call the "First Sale Doctrine". This, however, does break down in the case of digital copies, since these are distinctly different from physical products.
In the case of physical products, the creator should have absolutely no control over the specific instance of the product after it has been sold to the first buyer. That means that the buyer has the ability to share it or re-sell it when and how they see fit. This does not, however, allow them to reproduce -- make duplicates -- of the product; except in extremely limited Fair Use cases, such as archival backups; short excerpts for criticism, review, and parody purposes; and sampling for use in derivative artistic works (though this last is a huge gray area in case law).
The purpose of intellectual property rights (including copyrights and patents) is to incentivize creativity by rewarding it - do you reject this idea?
That is the
ostensible purpose, and certainly was at the inception of such laws. However, Intellectual Property laws have changed dramatically since their inception; almost invariably in a way that favours the corporations, with a few notable exceptions. Corporations have also fought very hard against any changes or legislation that puts ownership in the hands of the consumer, or benefits the consumer in any way.
One of the biggest examples of this is the periodic extension of the Copyright period; invariably done at the behest of major corporations in order to maintain exclusive marketability of legacy properties. Disney being the prime driver of this, with the recent extensions being pushed for the primary purpose of maintaining ownership of their Mickey Mouse character from devolving to the public domain, as it should normally have done decades ago. This does nothing to "incentivize creation" of original work, it merely ensures perpetual ownership of a particular work and its derivatives for the purposes of maintaining the corporation's ability to profit off it; while stifling creative use of the property by others in derivative works. It also effectively stifles similar efforts if they are deemed by the courts to resemble the original work too closely.
The only notable exception to this, aside from existing Fair Use laws (which the corporations have managed to make some headway against, though not destroying it entirely as they would like), is the "time shifting" and "space shifting" exceptions for copying.
Time shifting is the principle that allows the consumer to record a broadcast for later personal, noncommercial consumption; and was established by IIRC consumer video tape, although it applies to audio tape recording of radio programs as well.
Space shifting is the principle that allows media to be copied to play back on a different device using a different format. This is what allows a CD to be copied to an audio tape (for example, mix tapes), or for a CD to be ripped to a digital audio file to play on a digital audio playback device. It is also what allows native digital audio files to be copied to a standalone device or playback from the "cloud" without having to delete the original file off of the computer it was initially downloaded to.
Legislation on these contains some vague areas, and case law is not as consistent as we should want; but the principles are fairly firmly established.
Corporations have tried to quash the time and space shifting exemptions, as well as gut First Sale Doctrine, by insisting that a particular product -- such as a software application, music file, or video file -- is a
service that the consumer is
subscribing to, rather than a distinct product; and therefore not subject to these consumer protections. Case law has not, to my knowledge, been firmly established here; and some producers have gotten around that by offering their products via an online streaming service that attempts to block the ability of the consumer to create persistent copies; or by building in expiration of the product (in the case of software), or by requiring the product to connect to an online server to validate its use. And entire industry sprung up to produce Digital Rights Management schemes to allow producers to limit the ability of consumers to take advantage of time shifting and space shifting rights, under the auspices of "fighting digital piracy".
There were several instances where producers attempted to use a degradable physical medium (a digital video disk based on dyes similar to DVD-Rs, but less stable so that they would degrade after a short time), or a proprietary medium and player that contained a lock code to limit the number of times it could be played back, in order to enforce the re-classification of the product as a subscription service. These were, predictably, failures. Even the streaming systems have seen their limitations compromised by utilities that enable the creation of persistent copies. DRM encryption and lock schemes find themselves hacked.
And it's not just pirates that use these hacks to allow themselves to create copies. Legitimate owners also use them to allow space and time shifting normally restricted by the format, as well as the creation of backup archives, something that the corporate producers typically try to eliminate the possibility of. The most notable example is the use of "cracks" to allow the use of Sony software products without installing their invasive rootkit DRM by those who purchased the product legitimately, and found their computer system functionality disrupted by the DRM scheme. Sony was eventually forced to discontinue the scheme under the pressure of multiple class-action lawsuits, as it was effectively an exploitable computer virus, and semi-official backlash from the Department of Homeland Security. Worse, Sony was also found to have themselves infringed copyright due to using a considerable amount of unlicensed open-source software in the creation of the rootkit.
Intellectual property law at this point in time has very little to do with promoting creativity; only a tiny fraction of the legislation and case law still applies to this purpose. It's now predominantly about corporations protecting cash cow franchises from falling into the public domain.
If not, how can you square it with the free-for-all that file sharing had become?
Technology has at many points in history created paradigm shifts in how intellectual property is treated. You pointed out the printing press as a historical example. Better examples are audio cassette tape, and video tape. In both cases, the industry attempted to outright ban the sales of both to consumers; and failing that, to levy exhorbitant fees on the sale of blank media that would be paid to the the entertainment corporations. The same effort was made to ban MP3 players, DVR products, and other recording devices.
Interestingly, this is not exclusively limited to the digital age. First Sale Doctrine was originally developed to allow the re-sale, lending, and rental of physical media such as books and vinyl LP records. The continued existence of used bookstores is due to this doctrine.
Industry has had to adapt to the technology, and always has. Protectionist legislation has rarely been successful for long. Either the public simply ignores it, and legislation eventually catches up to the public; or the protected format is simply supplanted by a new one, and the issue becomes moot.
It seems to me the logic is that "if enough people want to do it, it shouldn't be illegal," an example of the tyranny of the majority.
Yes, but that's not really the issue here. The issue is that it's going to happen, regardless of what anyone does, and the culture needs to adapt, just as it did for previous technological changes.