Some people in the UK are very keen on the imperial system of weights and measures as a symbol of national identity, even though each of the units is pegged to the SI system and in fact affords the government little in the way of policy options.
Imagine if Greece, instead of leaving the Euro, left the SI and brought in floating exchange rates for the metro, the hiliogrammo and the defterolepto. I suspect the first result might be a massive revaluation of each of them. Now, you might accept the case for Greeks selling you 15 m of cloth (in SI) when you’d only asked for 10, but still argue that a country can’t redefine time on its own. However, surveys of time actually spent in the office show that the UK workers’ hour is really more like 4000 s than the officially mandated 3600 s, so something similar is going on unofficially here.
We can go further. We could introduce different peggings for different substances. At present, a tonos of feathers has the same mass as a tonos of spectrometer parts. If we introduced slightly different units for different substances, then we might find that a tonos of feathers has roughly the same mass as 1000 kg SI of feathers, but a tonos of Greek spectrometer parts was substantially heavier.