The only useful purpose served by making a loop antenna from coaxial
cable is to ensure capacitance balance of the loop against ground, so
sharpening its directional nulls and, incidentally of course, to
support the very thin inner conductor which would otherwise collapse
under its own weight.

The outer coaxial conductor has no effect on signal to noise ratio as
perceived by the receiver. S/N ratio depends only on what's contained
in the local field itself.

If there's any difference in S/N ratio due to use of a tuned loop, as
with a magloop, then it is due to the loop's very narrow bandwidth -
not the shield.
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Reg.