The written interview serves multiple purposes.
First, it is a response to a massive flow of applications. We can more fully and fairly assess those who show they are willing to do some work to be part of our company.
Second, it helps address bias. The written interview is not a resume, which a hiring manager would read through bias like "I recognise that university" and "I like that country". The written interview is anonymous work, which can be assessed more objectively. We get it assessed, twice, anonymously, in the common case. For my roles, more than 100 people at the company help me with this, and I'm grateful to them for the work they do.
Third, it helps us focus our resources. We have very light resume screening requirements - be a plausible candidate from somewhere in the world - but we spend a LOT of time on the written interview, and interviews. So for those candidates who show they care, they have insights, and they are quick on the uptake, we can spend a lot more time on them.
Fourth, it helps avoid repetition. We can share a written interview with interviewers later in the process, and they get a lot of context on the candidate very quickly. They don't always read it before meeting the candidate, but they can and they should.