How much could it cost to pay someone else to do this? Surely less than a doctor makes doing it... It can become its own profession. It's a separate skill - separate from what a doctor should be focusing on.
On a side note, it seems that a lot of professions would benefit from having an assistant - a thing that seems to have disappeared - if what I've seen in old movies in shows is to be believed. Another side-case of this is the fact that technical people tend to be promoted into management roles and have to deal with attendance and time-sheets - why not have someone else do it? The work only suffers.
The Scribe had a laptop and could look up whatever info was needed while the doc was doing his thing. If a scrip is needed the scribe types it in to the system and then the doc had to read it and approve.
Just keeping the docs hands clean from not having to touch a dirty laptop/iPad all the time has a health benefit I bet.