A LONG time ago I worked for Fidelity on the "MoneyOut" team. We processed distributions/rollovers/transfers/etc. Some were really easy to do. The forms were standard, the rules weren't too complicated, etc. Some were the exact opposite (this was especially true for small company plans that designed their own form/plan.
When I was hired, the team was really behind. Like a month behind. We worked a lot of overtime. The simple distributions pretty much everyone could do, the more complicated ones sat there in the queue until a more experienced person could get to them. I quickly became able to do those but even so, it took us quite awhile and many days of working through lunches and late to catch up to a daily queue that was manageable and something we could get through in a normal 8 hours.
I don't know if they still process "by hand" but I suspect if they do, that's what they're/you're dealing with. Not incompetence or lack of desire, just some short-staffing, training time, lots of people taking advantage of the job market and switching jobs, etc.