Not sure how centrifuged force extends grease longitudinally down the splines? If it’s not moving down there under the pressure of the gun then spinning it won’t get it there either.
I'll attempt to explain this without a diagram, but frankly I'm pretty dumb so this may not go well.
If the zerk is at the closed end of a cavity, and that is where grease is pumped in, even though it is non-newtonian it IS a fluid and with enough gravity it won't just pile up there on one side, it will get distributed relatively evenly as soon as the shaft starts spinning at any significant RPM. Now, as more time goes by with said RPMs, and as RPMs increase centrifugal force does too, the excess grease won't stay piled up there at the closed end of the cavity. The in-effect very high gravity environment (See note) will cause the technicaly-a-fluid grease to assume a "pool" shape, where the three sides of the container are the closed end of the cavity, the female splines on the outside, and the male end/splines/seal as the third side. The g-forces being so high will cause grease to migrate out between the male and female splines and past the seal.
Now for all of this to work there needs to be enough grease there. What is actually pushing grease to the relevant parts is more grease piled up behind it trying to get out of that high-gravity environment. If you only throw three pumps in that likely isn't enough to distribute around and actually coat everything.
Side note.. I got curious and did a little math. I'm not sure of the diameter of the splined section but guessed between 30 and 40mm. At 80mph vehicle speed (driveshaft 3437RPM on a 2008-15) it's between 198Gs (30mm) and 264Gs (40mm). Aka a lot of force to make grease flow.
Also interesting is how brilliant toyota's u-joint spider design is. For decades the US automakers put the grease zerk, if there was one, on one of the caps. When the cross is drilled, this allows you to pump grease into that cap and then get distributed around to the whole joint. But, it depends on the valve and tapered threads on that zerk maintaining integrity. If either fail, the high g-forces within that cap will let the grease drain out. The other three would be fine.. but that one not good.
For a long time toyota has put their zerk in the middle and cross-drilled the joint so that it can reach all four caps. But.. with all 4 caps being closed, they basically act like little bowls holding the grease inside, keeping the bowls full, no matter how fast you spin the shaft. The only way to get that grease out is to push it out from the zerk with another fluid.. generally new grease.
Anyway.. all of this grease distribution business makes sense in my head, but as mentioned I'm not the smartest by any stretch.