Accountant - agreed, my point was many people refer to 'accountant' where they mean bookkeeper. I do not see computers replacing good accountants - if anything it will make them more important as the better raw data gives them more ability to make a difference.
But I completely disagree on your description of what current accounting software can do. Computers are opening the post (email) for remittance advice, chasing short payments and reconciling the ledger. They flag over-payments but leave chasing them to a person - too much thought required on the communication. They also collate expense receipts and chase staff for the various tasks coded into workflow (singoff from immediate manager, tracking against budget and authorisation limit, flagging suspicious values to appropriate people, etc). Paper invoices are also handled - scan it and it's emailed off to manually assisted invoice creation (too much variation in invoices for risking automated loading). Oh, and all purchases are also directly exported to the bank where you can configure them to either just be paid or require final authorisation depending on how reliable you feel your setup is..
They already integrate with stock tracking systems and so eyes they do depreciate stock, handle damage and lost items. Stock isn't something I have firsthand experience managing, but I haven't heard any complaints. Timesheeting and payroll are also fully integrated and I know they both work well.
Current state... I see an opportunity to help someone out. I create a quote in the accounting software. I email that quote to them and if they decide to go ahead then they create a corresponding PO in their ERP system. That process automatically checks against signoff limits, obtains approval from direct manager, etc. That is then automatically emailed to me where the accounting software automatically matches it to the quote. I then deliver the work and get them to sign it off. Once that's done I click a button to convert the quote or the PO into an invoice, adjust if necessary and click send. Again now their system receives that invoice, matches it to the PO and emails my contact to validate the work was signed off as complete. Then it schedules it for payment and sends remittenance advice. That gets matched by my software which sets the invoice expected date. When the payment is made it reconciles against this invoice. If they don't pay then it automatically kicks off whatever workflow I choose to set up - friendly reminders by email with summary of outstanding and a note to me.
Sure, it's not perfect and there's still a need for bookkeepers. Someone screws up the reference code on the payment, accidentally double pays. Subcontractors who charge a different rate depending on which client they're working on, reversing out declined expense claims, client or supplier correspondence beyond simply sending out statements, etc. But compare it to say 5 years ago - I wouldn't feel very safe as a book keeper.