That is not a practical solution and an unfair burden.

As opposed to the law turning a blind eye to tools that facilitate illegal activity on a massive scale, while requiring everyone actually holding the relevant legal rights to take individual action against every infringement themselves, even in the face of blatant and repeated infringement by the same people using the same mass distribution service?

If you want to talk about impractical solutions and unfair burdens, talk to any small-scale, independent content producer who's seen something they worked on for months shared on-line and watched their profits evaporate. Not everyone in the content ecosystem is making big hits like Game of Thrones or the latest Taylor Swift single and at least benefitting from some extra exposure leading to more people buying the content with real money later as well as losing out to pirates who won't. Not everyone in the content ecosystem has full-time in-house legal staff to chase down infringers, nor the resources to actively monitor every major content sharing service 24/7 to intercept large-scale illegal redistribution in near real time.

Most people do not have that option at all.

Anyone who is on the Internet in the first place has that option. You can have control of your own web site for a fraction of the cost of a monthly ISP subscription, and you can learn to do it with a few minutes on Google, the help provided by your chosen hosting service, or asking your neighbour's 15 year old kid.

Aggregating many users makes publishing affordable to many and the filter-always rule goes a long way towards making that impossible.

Aggregating many users makes publishing affordable to those who want to benefit from publishing but spend literally nothing on it. Even if you have freedom of expression protected by law to some extent, that doesn't mean you're entitled to have someone provide you with a mechanism for expressing yourself to a huge audience, free of charge.

For example, YouTube is free to take down any video they like for any reason they like on their own service, regardless of whether or not any law actually requires them to do so. It's their service. If you really believe in promoting free expression, surely you should be in favour of more people publishing independently and under their own control?

In any case, you're dramatically overstating the effect of the filter-always rule as I understand it. From the description given in the article, it appears that the rule just says if someone has formally complained about a copyright infringement under the safe harbor system, and that complaint has not been disputed and therefore presumably the original copy has been taken down, then the same rightsholder does not have to keep formally complaining about the exact same material if it's uploaded again after being taken down the first time.

I don't see how this stops anyone from publishing anything, unless it's already been published, and that has been challenged, and the person who published it has not exercised their right to dispute the allegation of infringement. And the extra burden here is primarily on the hosting service, which is usually the huge beneficiary of safe harbor agreements already and still bearing far less burden than they otherwise would under the law.

How is any of this unreasonable, assuming a fundamental desire to reconcile freedom of expression with the legitimate interests of copyright holders that are recognised and protected by law in as fair a way as possible?