None of the axle motions happen in a perfectly straight line - everything moves in 3-D arcs. So kinematically - meaning you're considering geometry alone - none of the four locating links pivots precisely about the bolts that attach it to the axle or to the chassis. Instead, all eight pivots (two each for the LCAs, the UCA, and the PHB) need to allow their links to rotate in all three axes as the suspension moves. Ideally, and the way just about anybody who isn't working at the OE level would be able to analyze the suspension, would have every pivot back there being a spherical.
Tools for analysis at the OE level are orders of magnitude more capable (and orders of magnitude more expensive and needy of more input data) so let's just say they can predict how much bushing distortion is occurring and how much the axle location would change as a result and leave it at that.
When compliant bushings are introduced at the ends of the links instead of sphericals, distortion of a soft-ish bushing material is intended to accommodate that 3-D rotation. This is what allows Ford to use what I call 'cylindrical bushings'. The main rotation is about the attaching bolt center, as you'd expect. The smaller other two mainly occur within the bushing material. When the material is soft enough, this happens without generating any appreciable amounts of force or resistance and everything is fine . . . as long as they aren't subject to too much force. Should too much force happen, the axle may no longer be under adequate location control. Like wheel hop.
On the aftermarket side, off-axis rotations are generally assumed to be small enough that firmer bushing materials can be used. This would be for more positive axle location, with suppression of wheel hop or at least minimizing that being the main intent. But since nearly all cylindrical bushings are about equally stiff in all the other directions as they are in the 'good direction' that resists wheel hop, now you're generating "unexpected" forces as the bushing distorts to accommodate those off-axis movements/rotations.
As long as any off-axis rotations are small enough, it's still not a big problem. Sometimes that's a matter of link orientation in the car and sometimes it's up to the driver to limit the amounts of rotation by the way he drives. About here is where the simple poly bushings really start to get in their own way, where the movements developed by cornering roll working against bushing stiffness can create forces that are big enough to act as a virtual rear stabilizer bar . . . and that imaginary "sta-bar" can have an effective stiffness approaching that of the real one (this is why poly-bushed axle links/control arms aren't the hot tip if you're at all inclined to drive hard through the corners). Most times you'll hear this called 'bind', though it's really a case of 'induced forces'. The joints don't get stuck, they just get progressively harder to distort as required
Spherical pivots accept the off-axis stuff without resistance or developing forces in reaction - they don't care what precise axis orientation they need to be rotating about. Their main downsides are cost, NVH, and maintenance, and in most cases need to be considered 'wear items'. Not that poly bushings aren't 'wear items', but that's a separate story.
Sphericals do exist for both ends of the UCA if you look around a bit (hint: BMR arms, Steeda diff-side pivot). They will almost certainly transmit more noise from the differential back into the cabin.
Another hint: there are a couple of things you can do to poly to make them a bit more like OE rubber bushings without losing all of the 'good direction' stiffness . . . if you have a good idea what you're trying to do and if you're willing to potentially give up some bushing life. But I'm going to leave that as just a hint, at least for now.
Technically, sphericals are going to be better for the straight line stuff than poly ever would be for the corner-carving side. For LCAs, sphericals in one end with poly (perhaps lightly modified) in the other should be sufficient. I'm less sure about the shorter UCA being a good place for poly in a hard-cornering environment, although poly bushings there would work well enough for straightline purposes where you aren't throwing a lot of cornering roll or relative lateral movement at them. (Because the UCA is located above the rear roll center height, roll creates a little relative sideways motion that has to come out over the length of the UCA. Something similar happens at the LCAs, but by being longer the effect isn't as severe).
As a corner-carver (and not into drag racing or hard launches at all), I haven't bothered changing the UCA on my car. The LCAs are poly/spherical (Johnny-Joints, not Heims), and the PHB is still OE but with bushings that have been stiffened a little.
Norm