Scholars certainly argue normatively that copyright should be considered to be content-based, but that’s not a descriptive portrayal of how courts actually view the matter. You and others might think that copyright should be content-based, but what you can’t do is point to a single court that has ever held is.

I sure can:

When the RTC first approached the Court with its ex parte request for the seizure warrant and Temporary Restraining Order, the dispute was presented as a straight-forward one under copyright and trade secret law. However, the Court is now convinced that the primary motivation of RTC in suing Lerma, DGS and The Post is to stifle criticism of Scientology in general and to harass its critics. […]

Although the RTC may attempt to argue that “any public interest in obtaining information through media sources … does not supersede the rights of a copyright owner,” Emergency Motion at p. 44, copyright law, the First Amendment, and the fair use doctrine prove this is not always the case. […]

For the reasons mentioned above, RTC’s Motion for Preliminary Injunction against defendants Lerma and Digital Gateway Systems is DENIED and defendant Lerma’s Motion to Vacate the Writ of Seizure is GRANTED.

– RTC v. Lerma

So the court, in at least this case, acknowledged that copyright injunctions can be a content-based restriction, and thus unconstitutional under the First Amendment.

There’s also Suntrust v. Houghton Mifflin:

In this case, we have found that to the extent Suntrust suffers injury from TWDG ’s putative infringement of its copyright in GWTW, such harm can adequately be remedied through an award of monetary damages.   Moreover, under the present state of the record, it appears that a viable fair use defense is available.   Thus, the issuance of the injunction was at odds with the shared principles of the First Amendment and the copyright law, acting as a prior restraint on speech because the public had not had access to Randall’s ideas or viewpoint in the form of expression that she chose.

We VACATE the judgment of the district court and REMAND the case for further proceedings consistent with this opinion.[Emphasis mine.]

So, copyright injunctions can be a prior restraint on speech, and a violation of the First Amendment – because it restricts the content of the speech (“Randall’s ideas or viewpoint”).

Of course, this doesn’t mean that all copyright cases are “content-based” in the First Amendment sense; but it does mean that they can be in individual cases.

Furthermore, as you’re aware, Eldred did not even consider the issue of whether new copyright laws must pass strict, intermediate, or rational basis scrutiny. They were only dealing with whether the extension to copyright laws which already had a hundred years of case law to bring it in line with the First Amendment, would need to pass additional strict, intermediate, or rational basis scrutiny:

We recognize that the D. C. Circuit spoke too broadly when it declared copyrights ?categorically immune from challenges under the First Amendment.? 239 F.3d, at 375. But when, as in this case, Congress has not altered the traditional contours of copyright protection, further First Amendment scrutiny is unnecessary. [Emphasis mine.]

That is not the case with either PROTECT IP nor SOPA, which would grant the government unhindered powers to blacklist websites ex parte.

And, as again I’m sure you know, such schemes are unconstitutional, even in cases of child pornography:

The two filtering methods used by the ISPs to comply with the Informal Notices and the court order ? IP filtering and DNS filtering ? both resulted in overblocking. […]

Although there are strong arguments for the application of strict and intermediate scrutiny, the Court need not choose between the two because, even under the less demanding standard ? intermediate scrutiny ? the Act does not pass Constitutional muster. Under O?Brien, a regulation must further an important government interest unrelated to the suppression of free expression and the incidental restriction on First Amendment freedoms must be no greater than is essential to the furtherance of that interest. O?Brien, 391 U.S. at 377. The government has the burden of proving that the “regulation will in fact alleviate [the] harms [addressed by the regulation] in a direct and material way,” Turner, 512 U.S. at 664, and it has not met that burden in this case. In addition, the Act suppresses substantially more protected material than is essential to the furtherance of the government?s interest in reducing child sexual abuse. […]

The Act and Informal Notice process are not prior restraints in the traditional sense. They do not prevent speech from reaching the market place but remove material already available on the Internet from circulation. Alexander v. United States, 509 U.S. 544 (1993) (“The term ‘prior restraint’ describes orders forbidding certain communications that are issued before the communications occur.”) However, they are administrative prior restraints as that term has been interpreted by the Supreme Court. According to the Court, “only a judicial determination in an adversary proceeding ensures the necessary sensitivity to freedom of expression, only a procedure requiring a judicial determination suffices to impose a valid final restraint.” Freedman v. Maryland, 380 U.S. 51, 58 (U.S. 1965). Thus, if material protected by the First Amendment is removed from circulation without these procedural protections, the seizure is invalid as a prior restraint. […]

Based on the decision in Bantam Books and Fort Wayne Books, this Court concludes the procedural protections provided by the Act are inadequate. These cases require a court to make a final determination that material is child pornography after an adversary hearing before the material is completely removed from circulation. Under the Act, a judge is only required to make a finding of probable cause, he can make this determination ex parte, and there is no requirement that the publisher or distributor receive notice or an opportunity to be heard. […]

For the foregoing reasons, plaintiffs’ Motion for Declaratory Relief and Preliminary and Permanent Injunctive Relief is granted. Pennsylvania?s Internet Child Pornography Act, 18 Pa. Stat. Ann. Sec. 7621-7630 and the Informal Notice process used by defendant to implement the Act are declared unconstitutional.

Please note that the material itself had no constitutional protection whatsoever (they agreed with Aliance v. FCC that “No Internet speaker has a right to engage in these forms of speech, and no Internet listener has a right to receive them”). Despite this fact, the Pennsylvania web-blocking scheme, which was even milder than the ones proposed in SOPA an PROTECT IP, was unconstitutional under the First Amendment.

It was censorship. Just like these bills are censorship.