'Soft Eye' in climbing anchor construction

present it in a manner which has nothing to do with climbing so we can avoid answers to questions I'm not trying to find answer to

Interesting… the whole premise of your original question was clearly in relation to anchor systems used in recreational lead climbing.
Context is key when discussing knots and the material that knots are tied in.
You cannot escape context when discussing knots and their applications.

I wanted to know whether the integrity of a double bowline on a bight, when ring loaded only, would severely suffer from the rupture/tear/cut of a single strand
And the answer had been given already. #1080 Bowline on a Bight does have a vulnerability - and it is with its 'collar'. The risk is small but, it is a residual risk. The loss of one leg of the anchor will not trigger catastrophic failure. However, a rupture of any segment of the collar will result in catastrophic failure.
I do not seek advice in anchor building
And yet the whole premise behind your questioning is indeed anchor systems. You may not like the answers you are receiving - and so this may be a source of potential irritation to you - which you now seek to avoid.

The video link you gave is a good example of incorrect information.
The presenter refers to the knot as a ‘ring bend’. This is incorrect.
It is an eye knot.

A ‘ring bend’ can be found in ABoK at entry #1412 (and also at #296).

A bend is an entirely different structure - where 2 separate rope ends are united.
The presented also tries to provide supporting comments that ‘it is dead easy to tie’ - and; ‘useful all-round knot’… but nothing of any further substance is given beyond these limited remarks.

A point of fact is that Bowlines can be tied in a one-stage tying process. The eye knot in the video cannot be tied in a one stage process - it is not PET (post eye tiable).
This fact weakens the presenters case that his eye knot is easy to tie.. Furthermore, the concept of ‘usefulness’ is not substantiated to any degree. Bowlines are jam resistant on account of their nipping loop - and this property is useful. Bowlines are PET - and that property also makes them useful.

The loading profile of the core of the eye knot is significantly offset but, since both legs of the eye contribute tension force, it is unclear as to how well the structure will resist jamming in some of the newer sub 9.0mm EN892 dynamic ropes.

Does anybody have a definitive answer to this.
Keeping mind the crucial importance of context - it is hard to build a substantial case to support webbing/tape in lieu of accessory cord. Given that accessory cord is cheap, lightweight and readily available, there is no reason in principle why webbing/tape should be used in preference. Also, many independent testers have demonstrated the advantage of cord over webbing/tape to absorb energy. Given that the premise behind your original post was 'belay anchor systems' - it would seem illogical to avoid using accessory cord to build a solid and reliable anchor system (with no single point of failure). Given the ease with which a 'cordalette' anchor can be built - and the redundancy it offers (ie the 2 legs of the cordalette can be easily and quickly isolated with a simple overhand knot), it would appear to be the best overall choice. Cord also has a thicker cross-section compared to webbing - and so it is inherently more robust. This is one of the reasons why climbers use a rope - and not flat webbing - as their primary fall-arrest element. Imagine lead climbing with flat webbing instead of rope - and taking a fall...

#1080 Bowline on the Bight was never intended to be tied in flat webbing/tape material. The Bowline was intended to be tied in rope (a round cross-section material). That said, it is possible to tie knots in flat webbing - however the behavior of the knot under loading events will be unpredictable. Knot testing is typically done with rope/cord, not flat webbing material…and so it is extremely difficult to find any reliable test data. My point here is, why step outside of proven methods? What is the real reason behind wanting to use flat webbing/tape instead of cord?

In one of the links you provided on your original post: http://www.alpenverein.de/chameleon/public/07ace84a-bc33-615a-62a3-151e7b8b859a/Standplatzbau-Juli-2012_19947.pdf
Figure 25 (page 21) - left image… this is the preferred rigging setup using cord.
The image at right shows webbing/tape… which is not recommended for the reasons stated - chief amongst which is that cord is a better material for absorbing energy than flat webbing/tape.
One has to keep in mind that in multi-pitch lead climbing situations, there is a risk of a factor 2 fall right off the belay if the lead climber does not place the first piece of protection early and actually clip the rope into it (or that protection could pop and hence fail). This will result in a fall directly onto the belay - with severe impact forces. Cord will offer a better margin of safety than webbing/tape - because it will absorb some of the energy and you might live to climb another day.

There are several important reasons why you just want to create one main soft eye attachment point. The most compelling reasons are:

  1. It simplifies rescue - note that you should always rig for rescue (in other words, you should always assume the worst and be prepared).
  2. Building a cordalette anchor keeps your anchor rigging separated from your climbing rope - this ensures that you have the maximum length of rope available for the task at hand.

The soft eye created by an F8 or a simple overhand knot effectively isolates each leg of the anchor system thereby creating redundancy (no single point of failure).

Is there a compelling reason not to use cord?

Mark G