I believe it's because the cb will pick up running spin each time it hits a cusion (if they are hit sequentially). So if it starts with it, the extra it picks up won't substantially change the angles. But if no spin or opposite spin is used from the tip, the angles will change substantially when it hits the subsequent rails.
On top of this, there's also the self-correcting nature of the angles. With running side, the directional change (relative to no side) from first rail -> second rail is effectively the opposite of second rail -> third rail. This can be generalized past the first two rails such that any time you hit two adjancent rails (long->short or short->long), the effect is the same, but two opposites (long->long or short->short) doesn't work.
For most angles/powers the angles don't cancel eachother out perfectly, but the general trend still applies and makes it easier to judge. As a cherry on top, you'll also find out that its less sensitive to speed, due to the same aforementioned canceling out effect. I can explain it in more detail mathematically, but if you try it out on the table you'll get the same idea quite fast.
This can all be generalized to the idea of minimizing the margin of error in shot outcomes between different shot speeds/angles/tip positions. With the same concept, for 1-rail kicks you will find that top spin (or sometimes stun) is typically the most consistent.
A simple experiment to try: Set up some 1-rail or 2-rail kick shot, choose a spin to try, mark the CB/OB/aim and shoot it twice into the same aim spot but with soft vs. hard speed. Compare the difference in cue ball angles off the rails. Now try with a different spin, again shooting both soft and hard. You will quickly see which spins are more/less sensitive to speed for all kinds of shots this way.
