Totally does seem like something that can be nicely automated to some level. Even document tracking and associated metadata (like a list of participants and status of signatures per page, approval of document, etc) would help.
Now as to why we don't remove human lawyers from the process ... I think it's trust, mostly.
It's a bit like selling automated medical services. Your clients don't always have benchmarks for what's "good" legal work, much in the same they don't know if they're getting "good" medical advice, so it's hard to evaluate the quality of an automated service. And since there's always some chance the automation misses some edge case that a trained professional would have caught, if the stakes are high (medical -> life or death of a person, legal -> multi-million dollar lawsuit), clients opt to keep the lawyer (or doctor) in the loop.
For simpler or low-stake workflows though, there is direct selling to the client (see Clerky).