The distortion in S-meter scale-shape at very small signal levels, below
about S5, could be corrected very easily just by changing scale markings.
The meter scale would then end at about S2 instead of S-zero. And the meter
would indicate correctly as a wattmeter over the whole length of its scale.

But S-meter manufacturers are reluctant to do this. They consider it would
spoil the linear appearance of the scale at the low end and so lose
customers. How foolish they are!

Keen radio amateurs can change their S-meters into accurate instruments over
the whole scale just by scraping off existing scale markings and
re-calibrating with a fine-nibbed pen and black indian ink.

But on second thoughts, to save yourself the trouble, when using the meter
it's even easier just to visualise and remember where S3 should be marked on
the meter scale.
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Reg, G4FGQ