MK- Please elaborate. I am under the impression that:

1. A random-length "inverted L" wire antenna with coax lead-in is a
good
choice for a simple, effective receive antenna for 1.8 to 30mHz
listening.

It's ok for general use. I'm not against random wires. Just RHF's
description of why or how they work...

2. That the matching transformer, with proper ground, is a simple,
practical, easy way to mitigate extraneous RF noise.

The matching transformer has nothing to do with it. The ground is
used as a method to help decouple the feedline. It's the decoupling
of the line that mitigates common mode currents. All the matching
transformer does is change impedance. But impedance/ SWR, etc,
have *nothing* at all to do with common mode currents flowing on
the shield. Nada. Zilch. The only reason people use the transformer
is to provide a better transfer of power. But it's almost always
overkill.
The use of one can pump up the S meter, but it rarely improves the
s/n ratio. In some cases, the transformer can actually degrade the
signal if the original match was better than the new one.

Is there a better single antenna that covers the HF spectrum? And what
are
other ways to decouple the feedline?

Dunno. Just depends on the needs, path, time of day, freq, etc, etc.
No one antenna is best for everything. Thats why I have several.
For general multiband use, I like paralleled dipoles fed with a single
coax.
A 1:1 balun or a coax choke at the feedpoint is used to decouple the
line.
Some like a dipole fed with ladder line and tuner. The dipole would be
cut for the lowest band to be used.
Some like a large loop fed in the same manner. There are a zillion
antennas that can be used. It depends on the antenna, etc, but with
most
systems, baluns or chokes are the most common decoupling devices.
With elevated ground planes, the radials help decouple the line, and
extra "decoupling radials, cones, sleeves, etc can be used.
With the random wires, grounding the shield, or chokes are commonly
used. But the use of ground as a decoupling aid is only used on
incomplete antennas like coax fed random wires, ground mount verticals,

etc.. You won't see that used on many "complete" antenna systems.
MK