I have sometimes relied on a mechanical connection to provide a ground (like the case of grounding a tone pot through the control plate), but try to avoid it because those mechanical connections are where corrosion often appears as a guitar ages. And sometimes they simply come loose.
The only time I regularly rely on a mechanical connection is when there are simply too many wires already, or when soldering isn't necessarily the most reliable method. (Amp chassis grounds are a good example. It can be tough to get a good solder joint, so a lug tightened down is a good solution.)
I don't like those rings clamped to the pickup baseplate or bridge with spring pressure. Soldering to a baseplate is easy enough, and it's too easy for dirt, corrosion, or other junk to ruin the tiny electrical connection you get between the bridge and the screws that go to the baseplate.
I also don't like to daisy-chain grounds. If one ground goes bad, everything down the line is going to be affected.