Can one switch from the declared field of study in his SoP to another after acceptance?
(I'm a full prof at a top-5 American CS department, with a PhD from Berkeley.)

Yes, this is a common model for admissions in large engineering departments.  Admissions committees will assume that your statement of purpose accurately reflects your research experience, research interests, and professional goals.  Applications that describe interests in more popular areas (for example: machine learning) will face more scrutiny and stiffer competition than applications that describe less popular interests.

In the short term, this is important for funding decisions. Most CS PhD students at Ilinois at Berkeley are admitted with RAships, offered by individual faculty from their grants on specific topics.  We need strong evidence that you have the requisite background and interest in that research topic before offering you a job to work on that research topic.

In the longer run, this is important to make sure that the department will provide incoming students an environment that builds on their strengths.  We don't want to admit students who won't thrive, and we want to make sure that every incoming student can find an advisor, without overwhelming the faculty.

And yes, of course, PhD students can switch areas after they've been admitted, provided they can find an advisor in the new area.  After all, it's the student's degree, and the universe laughs at detailed plans.  That's why actual admissions decisions (in my department, at least) are made by a committee that includes faculty in all areas, rather than by the individual areas or individual faculty acting alone.  It's not enough for me to say that I would be happy to advise and fund a PhD applicant; there has to be strong evidence that the student will thrive even if they switch advisors or areas.

That said, it's a really bad idea to feign interest in a less popular area to get your foot in the door, and then try to switch to a more popular area.  As the Systers post you link to says: Popular areas have popular advisors.  Students who expressed interest in a popular area in their SoP have already been vetted by faculty in that area; students who did have not.  In practice, switching may not be possible.  And then you're stuck in a department that doesn't let you do what you really want to do!

Also, while allocating admissions slots to areas is a common model for admissions, it's not a universal model. Every department approaches admissions differently.  Some departments admit students under a general banner of excellence—under the quite reasonable assumption that most PhD applicants don't know what they want to be when they grow up—and then have everyone go through a common core of classes and group rotations.  A broader admissions model allows departments to take more risks, by admitting promising students who genuinely do not have specific research interests yet, which can lead both to huge payoffs and to more dropouts, but it can also put significant strain on the faculty in more popular areas.