Unfortunately, some publications use a double-blind review process, where checking whether the authors have published similar content before becomes more difficult: you'd have to figure out who the authors are first, which kind of goes against the idea of a double-blind review process.
But of course, when the double-blind review process is not used, then it makes perfect sense for a reviewer to check the authors' other published work. In journals that require a certain percentage of original work, I don't see any other way.
If all papers were indexed by a full-text search engine, you could simply pick a few sentences that sound unique and search for them across all publications. It's not like self-plagiarism is more important to detect than regular plagiarism :)
Or journals could just submit all papers to the plagiarism-detectors used for undergraduate work, like Turnitin.
But of course, when the double-blind review process is not used, then it makes perfect sense for a reviewer to check the authors' other published work. In journals that require a certain percentage of original work, I don't see any other way.