Why do admissions committees consider the Statement of Purpose to be important? Anyone with a command of English should be able to write a Statement of Purpose, in principle, so it seems a poor way to compare applicants' research potential. If I were to judge an applicant (obviously I've never been in this position), I would much sooner at grades than at their Statement of Purpose, simply because grades cannot (in general) be 'faked'.
Why do admissions committees consider the Statement of Purpose to be important?
This question assumes they do consider it important, but how it's actually viewed varies enormously between departments. In mine, it's not considered particularly important for most applicants. If your statement is pretty good, then that's good enough (nobody was ever admitted by writing a great personal statement). However, it can matter in special cases:
It gives you a chance to address anything non-standard or potentially worrisome about your application. It can be really valuable for you to make a case for why these things are not in fact a problem.
It gives you a chance to shoot yourself in the foot. For example, applicants occasionally sound like arrogant jerks, demonstrate that they like to talk about mathematics they don't understand at all (without admitting their lack of knowledge), or reveal that they have no idea how graduate school works. The first two are major problems, and the third is worrisome.
It can also be helpful to learn things like the intended specialization or advisor, but we ask for that elsewhere on the application as well.
If you apply to a department that takes this approach, then you shouldn't stress out too much about the statement of purpose. But of course other departments may do things differently, so you can't relax entirely.
One excellent reason for requiring a statement of purpose is to make sure that applicants have "done their homework." Have they taken into account who works in the department, and what can be done there? Can they formulate ideas for projects they'd be interested in working on? Furthermore, writing ability is a very critical factor for success as a researcher; someone who writes a very poor statement of purpose is likely to have a very difficult PhD candidacy.
Grades are somewhat objective, but they're also subject to a lot of external factors ("grade inflation," "scaling," sample size, and so on). But that doesn't mean they're not also considered. All parts of an application are usually considered, although the weights given to the various factors may differ greatly between departments.
It may be simple for some to write good English but to actually write something valuable is a lot harder. There are of course no perfect single tools to evaluate applications so having a multi-pronged approach provides some improvements in the weeding process. Grades provide insights into some aspects, particularly someone's ability to perform on exams. Such ability is not necessarily equated with ability to, for example, think critically or creatively (we do of course not know of the assessment methods underpinning the grades). A Statement of Purpose provides insights into the person's own insights into a research problem or field. Hence combining these two aspects with CV, letters of recommendations or whatever else is required, forms a more complex picture of the applicant than what each and every part of the application does on its own. The Statement will perhaps be the part that most closely reflects on the persons ability.
As a complement to other useful answers, I'd say that it is not possible to "fake" a good personal statement (unless one enlists already-successful mathematicians, and, even then, it's not clear...). The issue of grammatical correctness is non-trivial, but minor. The tone, the affect (all the more subtle in written language), speaks reams. The implied/assumed context? Etc, etc, ... And, indeed, all the better that most applicants do not effectively see how to "game" the personal statement. That's what I look at first, for graduate admissions. :)