Where it came from (history)
The Airbus-style airspeed tape on the A320 onwards comes from the A310 (Flight, 1987).
The present scale convention is similar to that used on the A310, and pilots have obviously readily adapted to it, but it does show that it may take a little time to shake off an old, ingrained response.
What the author is referring to is the speed-deviation indicator, an indicator like that on the 767 shown below that shows how fast/slow the plane is compared to the target speed.
The A310 had this design when Thomson-CSF (later became Thales Group) took over the forward-facing crew cockpit (FFCC).
Thomson-CSF has been developing its A310 CRT symbology in close cooperation with Airbus and the customer airlines, and many details have changed since the company's selection as A310 supplier in September 1979 (Flight, 1980).
Based on the above, Thomson-CSF reached the final design through usability engineering.
The A300 had a circular attitude indicator. The A310 change was to crop the sides to allow for an airspeed indicator.
The electronic attitude director indicator (EADI) which forms the basis of the PFD is no longer round, allowing more airspeed information to be presented on the sliding scale on the left.
The aircraft's indicated airspeed is shown by a yellow circle, the arrow through it indicating the speed trend. The airspeed symbol and trend remain stationary while the scale moves.
My opinion: This is the closest thing to the old "clockwork" cockpits, where an instrument's hand position was enough to glean the required information. Here the pilot would keep the yellow line (or circle on the A310) away from the too-slow and too-fast regions.
Not just Airbus
Below you can see the different versions on the 737 Classic, the one on the right featuring the "rolling digit cursor."
Something I found during my research I think is worth sharing about Airbus' philosophy that I haven't heard before:
The coach driver gives a command and the horses take care of the road, the A320 pilot makes a control input and the aircraft takes care of the flightpath (Flight, 1986).
I think the Airbus airspeed tape follows that, showing only what's relevant at a glance, as Radu094 wrote in their answer.