Knife randori

I can see some potential pros and cons (pun intended) in the police knife video. Let's take them one at a time.

Potentially good things:

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  The defending officer protects his gun side (assuming he's right handed and the baddie attacks right handed.) Protecting the gun side of the body is fundamental in police training, and that can lead to odd, one-sided techniques just as in SMR jodo (in Japan there were no left-handed swordsmen so the system is mainly one-sided).
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  The defending officer may be assuming the presence of a partner, in which case, if he can get a nominal control of the attacker then the partner can assist. He may also be able to assume the presence of knife resistant body armor (not that that would protect his hip flexors).
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  The defending officer does end up in a mechanically superior position with respect to the attacker's base of support (sure uke could stand differently, but just go with me for right now).

and the potentially bad points (besides the ones y'all have already mentioned):

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  The form that the officers demonstrate is force-on-force situation, which may be intuitive and easily teachable but strategically undesirable.
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  The defending officer has to make one or two iffy hand switches.
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  Though the defending officer has good mechanical advantage, it would be easy for the defender to scoop him with something like taniotoshi or gedanate or sukuinage.

Now, the S.T.A.B. video clears a lot of this up. In the police video we only see one repetition of a demnstration form of the thing, but in the S.T.A.B. video we see several different people doing variations with different levels of resistance. So we have a lot more info. I'm sure not trying to sell you on S.T.A.B. but I can see a lot of good in it.
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Basically what the guy has done is built his system around one aikido technique - maeotoshi.  He's got a set of techniques all related to maeotoshi. The shoulder hit may be seen as a sort of testing the attacker to see if he'll fall for sumiotoshi. The guy didn't demonstrate it, but gedanate would work well from this situation. He does demonstrate a form of ushiroate. Uke is primed in much of this video for deashibarai or kosotogari. And the guy does show smooth transitions from an inside clinch to maeotoshi and from maeotoshi on one side to maeotoshi on the other side.
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The knee to the peroneal nerve is a pretty good addition to the system. It doesn't over-commit tori but it can hurt and it can give tori a good offbalance for maeotoshi or gedanate. Another good form of the same thing is for tori to stand on uke's near foot, pinning it to the ground. I also saw a head-butt in there.
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Several folks mentioned that the instructor got cut up a lot in his demonstrations. I don't know how long these folks had practiced this system, but the students were doing pretty good. I didn't see them getting cut up like the instructor. Plus, we've all heard the old adage to expect to get cut.
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Overall, I think the police video was a pretty poor demonstration of an overall pretty decent exercise that I'd like to play with some, sort of as a hyped-up form of randori. I've seen a lot of what I'd consider a lot worse.

The standard disclaimer applies - I'm not a knife fighter - I don't even play one on TV. Fortunately we've got a certified (certifiable) knife guy working out with us. Rob, maybe you could expand on what you think of these videos and what you see of this system's potential.
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There's still more of my thoughts to come on the knife defense topic. Stay tuned...