If this procedure had been around (and flown) by Birgenair 301 and Air France 447, then they and their passengers might be still around to talk to. Air Asia 8501 is looking similar.
When I did the training, it was explained much like the quote from Boeing near the beginning of the thread. It’s a two-sizes-fits-all get-you-out-of-the-doo-doo procedure for when the aircraft is misbehaving and you have picked it up late or are uncertain as to exactly what’s happening.
Having an insidious pitot/static issue in IMC and turbulence is very different to a sudden loss of airspeed indication when you’re fully stable on short finals. However, if you make a mess (however small) of the rest of the approach and landing with your own version of “airspeed unreliable”, the first question will be: “Why didn’t you follow the QRH drill and sort it out later?”
I know this seems like “dumbing down” and I myself make sure I know enough performance attitudes to cover most phases of flight without having to look them up but from a point-of-view of overall safety, this procedure will as near as possible 100% keep you flying and under control. As professionals we are paid to follow (within reason) the safest path, not the most personally satisfying or neat one...