Once again I'm obviously misunderstanding your point. I haven't found it necessary for the 2m/440 one at my roofline, but my 3/8x24 HF mounts usually have either a capacitor or a small coil at the base...
Exactly: between the antenna and ground. You have to put that across the
mount,
meaning that you can't just swap antennas for different bands
on that mount without
also changing the shunt element. (Though you might have a value that works for a couple
adjacent bands.)
You can put a quarter wave (or some variants) on a 3/8-24 mount because it only requires
one connection: to the center of the coax. But if you want a base where you can switch
between, say, 1/4 or 1/2 wave antennas for the same or different bands, you run into a
problem because the 1/2 wave antenna requires a ground connection for the matching
network, and there is no ground available
on the antenna side of the mount.
Most commercial VHF/UHF antennas that are longer than 1/4 wavelength require a ground
connection for the matching network. (You can argue about the 5/8 wave, where lengths
that can be matched with just a series coil and low SWR have less than optimum gain.)
This is particularly true of multi-band antennas. That's why the range of options for the
3/8-24 mount is limited. The NMO mount (or the SO-238 style) provide a ground connection
in addition to the coax center conductor, so you can build any required matching into the
antenna rather than requiring a particular value to be wired into the base when you swap
antennas.
Several companies make an adapter that goes from an NMO to 3/8th mount but NONE that I know of that go the other way around!

And this is exactly the reason: The 3/8-24 is a
single wire connection to the center of
the coax. The NMO is a
two wire connection to the center
and shield of the coax.
You can't convert from a 3/8-24 to an NMO unless you have some way to run the ground
connection to the NMO mount.