Having worked in a data center. The "walk around with the clipboard" kinda still happens. Except its a tablet that syncs up with an actual database instead of lots of useless paperwork. Easy enough to look just as busy with the tablet.
You can't stamp a tablet with your hanko, and faxing it is difficult as well. A tablet would require changing a lot of established procedures.
Could there one day be a stamp that also has an RFID/HSM inside, that signs things digitally but gives the same UX?