Flare aside, there are really two important things to consider with respect to the usefulness of the square 4x4 CPL along with an ND grad (with no independent rotation).
1. polarized light from sky is fairly consistent in its orientation with respect to the horizon. This is why, once you dial in your screw-in CPL it generally doesn't need further adjusting as you move the camera around the compass (assuming level orientation is maintained). That is also why the LEE 4x4 "works" even after having aligned an ND grad to the horizon: LEE makes an attempt to orient the filter to its geometric sides in a way that approximately corresponds to polarized light in nature. there is some variability here, to be sure, so you might not be dialed in exactly to "maximum filtering", but you will see some benefit.
2. Polarized light from reflections is random in its orientation which means it is very likely NOT going to correspond with polarized light from the sky. Thus, some precise rotation of the CPL will be required to achieve the desired results to remove reflections from rocks, surfaces of water, etc. For this reason, a round, screw-in CPL mounted onto the LEE 105mm adapter is the only viable solution.
3. I don't see the benefit of pointing a square CPL at the sun, unless you are using it as an ND. There is very little if any polarized light in the sky (except at the very wide angles, in which case the effect is quite non-uniform across the frame) and you have virtually no chance of controlling reflections from water/rocks, etc. due to the lack of rotational control.
4. By far the most flexible and effective use of the square CPL will be in the situation where an ND grad is not used, and you can rotate the CPL however you want, to produce the desired result, with or without a solid ND such as a big or little stopper.
5. the most stunning work seen in this thread appears to avoid the very severe flare conditions that Jalal is pointing -- bright sunlight overhead and even with the sun nearly in the frame. This seems to be a valid disadvantage of the square CPL
6. the vignetting advantage afforded by the 4x4 CPL appears to align with those use cases where the CPL effect itself is the most non-uniform (at very wide FOV)
7. If one's work depends on use of both (a) an ND grad and (b) use of a CPL to control reflections, then the best solution is one that provides independent rotation, i.e. the (more expensive) 105mm option. However, If one is truly dedicated to those UWA situations where the polarizing effects are quite non-uniform across the FOV AND those same situations are not disadvantaged by the flare properties of the exposed-edges, then the 4x4 represents a cost advantage
I guess I'll keep looking into the 105mm options, esp. the value of coatings (flare/ghosting), and filter thickness (to avoid vignetting).
5D mark iii, EF-24-105mm f/4, EF 70-200 f/2.8L IS II USM, Speedlite 580 EX II plus 3x Yongnuo 568EX, photoflex 60" white umbrella, Westcott Apollo Orb with grid
400mm on a 1.6x body is still 400mm. sensors do not change lens physics...