Because strong written skills are a requirement of the job you are doing - it’s as simple as that and a non-negotiable/something firms aren’t not willing to compromise on.
People have been getting people to write things for them for decades.
Freshfields used to have a hand written application form in the 2000s - even back then there were people who used to pay others to write it for them not just for content but also for nice eligible hand writing.
Even if people aren’t paying someone to do it, parents/friends/mentors and even places like this are informing people how to write applications. And yet plenty of people still can’t write a good application - I’d say 70% of applications fall down because of poor written skills - more so than any other criteria. Some of the pay for services are not very good either - I have seen some examples online and I could tear apart the “revised” application for errors, crappy/convoluted language, poor structure etc. Paying someone to write it for you isn’t always going to lead to success.
Firms will often have other stages in the recruitment process that will pick up these skills again and verify their ability. Even if there isn’t a written element to further assessments, there are strong links to being able to do something like a case study well and having to pull together your own application well too.
Many times I can spot when someone has written an application for someone else though, and I have also been able to spot when it’s been written for someone else and the person doesn’t match up at interview.