climbing rope stretches.
I would be very surprised if this does not result in a smaller cross section.
First : the "knot implant" is meant to be pulled out of the nub
easily, by hand - and it is a very short segment of rope, so the net result of the stretch you mention on the area of its cross section is almost ZERO...
Second : We would be GLAD to be able to stretch this segment, and force its cross section to become smaller ! This would had enabled us to pull it out of the nub more easily.
What dL said is that the "knot implant" can not slip out of the nub easily, because, to do this, it has to pass through different rope-made narrow "gates", which squeeze its sides towards different directions, and "flatten" it accordingly. This continuous change of the shapes of "all" cross sections, of the one after the other, as they pass through all those "gates", consume energy, so it makes the movement of the entire segment more difficult. Which is true - but, provided that we do not need to pull out the "knot implant" very quickly, the material of the rope can "flow" through those "gates" without much difficulty.
How do I know it ? Because I had tried to achieve
the exact opposite, with not much success ! I had seen that, however tightly woven around a more or less "straight" ( re. the path it follows ) segment a nub is, it can NOT grip / nip it very efficiently ! The very few exceptions are the single helical coils ( the "nipping tubes" ) of the climbing friction hitches, the double, cross-gartered helical coils of the
rat tail stopper-like hitches, and the adjustable loops based on the opposing bights mechanism. Provided that the "tight knot" into which we "implant" its Tail End is not one of those few knots,
all the other knots, however tightly woven they might be, are not able to nip a penetrating segment of rope so efficiently that we will not be able to pull it out of the nub easily, by hand...
Now, your comment about stretching would had made sense, indeed, in the following hypothetical situation : After we pull out and remove the "knot implant" from the nub of a tight knot, the cylindrical "hole" which remains is immediately "filled" with the material flown into it from the nearby segments, which become less stretched, so the area of their cross sections becomes larger, so there is this material "flood" which covers any remaining empty space, and the knot becomes, again, as untiable as it was before the removal of the "knot implant". Well, things might had been like this, but they are not. The segments of the nub around the "hole" do fill in the void, but, doing this, they become able to "breath", and so the whole nub becomes less dense, less tight, and more easy to untie.
There is a simple way to PROVE the value of this idea, but I had not refereed to it, because I know that it might sound alien to dL. and the other practical-knot-fundamentalists of this Forum...

Instead of ONE "knot implant", insert TWO, or THREE, or as many as you wish ! At the end, after you would had pulled out and removed them, the nub will become as loose as you wish...