I don't want to discount the fact that this would increase the bowline's security and make for an easily-inspected knot, but the backup double overhand knot around a leg might not be as secure in certain types of line as it might first appear as it lacks some structure to press firmly against to prevent springing open.
While one can read of some rockclimbers testifying
to the loosening of a
strangle tie-off, such that
I've mused about suggesting a
double strangle (as it
will get one full round turn clear of changing direction
in tucking back through the nub), a well-set
strangleshould hold. BUT, (1) it doesn't ensure that the
bowlinedoesn't itself loosen, all so well --it's not easy
to tiethe
strangle snug to the
bowline, though one
can work it so by means of pulling on the collar, after
the knot is tied (but that will enlarge the eye)--;
and (2) if tied around an eye leg, it fills an area that
might not have much room (the small eye of the
climber's tie-in comes to mind) --in this case,
the tail can be pulled away and tied off to the
SPart. (A point you make, too.)
Similarly, when people try to make a double fisherman's knot less jam-prone by putting a reef knot in the center, it really reduces overall security.

How can the (so-called)
"square fisherman's" be even AS
insecure --let alone more so-- than the
squaREef knot itself?!
(I do have some inclination to recommend that the center
knot be the
thief, in thought that it will slip until
pulling those back-up "safeties" (i.e., the
strangles)
into the nub and getting them greater security, thus;
one needs to have pretty evenly distanced back-ups
so they abut simultaneously the center knot.)
--dl*
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