I have a set and I used one of those to clear the holes on a motherboard after pulling out the capacitors near the CPU (VRM section).
On those capacitors, the thermal mass is too high for solder wick and the solder quantity is too small to be sucked in a wick anyway, and the hole diameter was pretty much exactly the diameter of the leads (it was hard to put replacement capacitors in).
Without a desoldering gun, I basically put a drop of solder on my soldering gun tip, add solder to both capacitor leads and pull the capacitor out. BUT, as I pull the capacitor out, some solder gets into the very tiny holes and it's hard to remove.
So I just take one of those needles out, put it on the other side in the partially blocked hole, add MORE solder on the other side for thermal transfer and gently push on the needle from the other side (the needle is stainless steel so it doesn't get solder sticking on it). As the solder on the back side of the board gets hot and liquid, the needle makes its way through the board without damaging the through hole.
But you do have to be careful, it's possible to break the walls of the through hole or lift pads.. you have to be gentle. So it helps to have something like this around, but a proper desoldering gun like Hakko fx 808 would do the job.
I used the one on the far right. The construction quality isn't great, as you can see the needle bent a bit and the material in which the needle sits is weak, the material gave up and the needle went inside the plastic about half way in my case. Still usable and in the picture I just pulled it out back to more than the original length as you can see from the other needles.