There is no need to filter out AI-generated statements of purpose.
Even without AI, it is not reasonable to assume that applicants have generally written their SoPs all by themselves. They have received substantial input from others, or even have had someone else writing the entire thing for them. The spread of LLMs might actually be beneficial here, because it could lessen the difference between applicants with friends or family that knows how to write a good SoP and those that don't.
Contentwise, an AI-generated SoP will probably read well, but very much generic (because it is going to mimic typical examples of SoPs available on the internet). To a large extent, LLMs are bullshit generators: They create text that sounds good on first glance, but they don't really have coherent arguments. Thus, I can easily believe that a LLM can write a decent SoP, but I'd very surprised if they produce a great one.
In conclusion, if AI-generated SoPs might have a significant impact on your admissions process, there is probably something wrong with the process. The solution is to improve the admissions process, not to try and filter for AI-generated texts.