Your post is a perfect example of why AI "ain't ready for prime-time":
1. The hood, without the ground strap, is not electrically isolated due to incidental points of contact like the hinges and the latch. 2. Current is not flowing through the hood because nothing uses the hood as a ground path (barring installation of some accessory that does.) 3. There's no ground strap to the chassis, so saying that the hood strap is required to ensure "that the hood and other parts of the vehicle are at the same electrical potential as the chassis" is silly. If the chassis has no ground strap, the hood strap can't ensure that.
Seriously? 12V of potential isn't enough to create a shock hazard. That's why you can touch battery positive with one hand and battery negative with the other and live to tell everyone how tough you are.
Again, no stock component relies on the hood for a ground path and "crucial" is utterly ridiculous. However, as I said, the ground strap helps contain RFI sources to the engine compartment, so some radio noise (especially on AM radio channels) is possible with a missing ground strap. FM is generally not affected by that RFI, though.
What a vague statement that means nothing if you parse it out. How does the ground strap prevent corrosion? How does it prevent damage to the vehicle's electrical components and wiring? Hint: it does neither.
I guess if you have a high concentration of stray gasoline vapors and something causing the hood to become charged (usually rubbing something on it), this might help prevent a fire caused by electrostatic discharge, but those conditions would be a freak combination of weirdness.
Look, I'd definitely run a ground strap. However, without one, you're unlikely to notice any issues, especially an issue with an O2 sensor. In fact, from the picture you posted, that ground strap is likely working well enough because it doesn't look like it's disconnected completely; rather, it looks like it broke and was tied together, which is likely good enough. By the way, to tell if it's good enough, just use an ohmmeter with one probe on each end of the ground strap. All is well if the resistance is close to zero (a few tenths of an ohm).