Mostly, I’m an advocate for as full a range of motion as possible, whatever movement we’re talking.
So why only go to parallel? Research (https://www.ncbi.nlm.nih.gov/m/pubmed/24662234/) repeatedly shows that the heavier load which can be managed at a shallower-depth-squat improves the rate of strength and size development IN CONJUNCTION WITH full ROM squats.
As long as we pair this with full ROM days, I believe we curtail the risks involved in exclusively training partial ROM (competitive female volley ball players had a 20 year trend toward very high ACL injury incidence when they were training only partial squats, even though they were increasingly stronger).
Have a rock bottom day. Have a parallel-ish day at about 25% heavier. The strength curve is better AND we gain skill, ability, and readiness in extreme ranges as well.
In the video (https://www.instagram.com/p/BupG9CrnSBl/ ) I'm squatting to a 14 inch box with this Hatfield variant. So far, I'm unclear what weight I'll be unable to move (perhaps in excess of 600lbs), since the safety-squat/yoke bar allows for a very different experience. I'm still testing it out. Contrast this against my freestanding rock bottom squat (4 inch box), which I would never take to a single rep maximal effort, and have never gone beyond 405lbs.
The research aside for a moment, I have always trained both extreme depth and partial depth. In my mass-gaining days, using both modalities throughout a week or month certainly appeared to expedite the growth of size and strength.
With regard to the Hatfield variant, I have high hopes for it. There are always real physical barriers to progress. As such, the progressive overload principle can sometimes be fleeting as far as implementation is concerned. The psychological barriers are tightly intertwined. That is, do you actually train to your true potential if you know the effort to do so could land you buried underneath a bar? Even hardcore lifters give up as the stakes rise. The Hatfield variant address this interestingly. First, simply reaching out and holding onto an external brace is psychologically less stressful than the sense of swimming in an unsupported sea with 500lbs sitting on your spine. Second, you could, in fact, pull on the bar, lending a little assist when the legs begin to "fail," giving yourself a sort of forced negative experience without a spotter. You are the spotter. You know precisely what he'll do and when. That is a big deal. As such, I have to recommend this one for the compromised populace on one end of the spectrum and the advanced athlete on the other. I could see it as valuable to absolute novices needing corrective exercise application, intermediates for technique, and elites to squeeze out that next 0.01% improvement.
It's no wonder this variant, Hatfield, hails to one of the greatest contributors to modern sports training, and who himself set a world record squat over 1,000lbs at the age of 45 years old.