We all know the tale: You find a spiffy new weapon, you go out and use it, and find that your damage is abysmal. Then you realize it. Your skill with this weapon is 1! Thus, you're forced to go trudge off to find some grey or green mobs to solo and thwack mindlessly for a few hours until you can finally get some decent damage out of the supposed "upgrade" that you were so pumped to get a few minutes prior.
One of the ways people have made this strange little grind somewhat bearable is by using the servants out in the Blasted Lands. Because they can't die from normal weapon strikes, you can simply set yourself in front of one and swing away. If you're max level or if you have a self-healing proc or ability, you can spend a long time just wailing away mindlessly at the guy, leaving one eye on the screen while you do other things. Some people have even been so ambitious as to drag one of them to Stormwind for a skilling up free-for-all in the trade district.
Unfortunately, it looks like the ride's over. People are reporting that the Servants are no longer giving skill ups, even after 10 minutes of wailing away on the mob. There's no blue post confirming or denying the change as of this writing, but if it's in, it would seem to be deliberate.
From a certain point of view, using the servants to skill up is a bit cheesy. They can't die, but they can't hurt you much either, meaning it makes a long grind that should involve fighting multiple enemies easy, if not too much quicker. But at the same time, this should also make Blizzard realize how annoying the whole process really is.
World of Warcraft has taught us that it's OK to have somewhat instant gratification in an MMORPG, and that not everything has to be an endless grind before it's useful. Weapon skilling seems to be a useless artifact from the old Everquest era. But then again, in Everquest, you had to skill up magic use too. Imagine having to cast rank 1 Frostbolt a few hundred times as soon as you leveled up just so your shiny new rank 10 Frostbolt didn't fizzle or fail to hit the enemy 9 times out of 10. Seems crazy, doesn't it?
Consider it the same with weapon skill. It feels epic to claim a powerful sword from the swiftly cooling corpse of Archimonde. It does not feel epic to return to a lowbie zone and use it to kill Defias Bandits for an hour before you can actually do any decent damage with it. Removing the ability to skill up on invulnerable mobs is just removing an invention born of the necessity of conforming to a faulty system. Removing the system itself is the best way to move forward, and an expansion Beta is probably about the best time to make it so.