"why is she building tank right now?"
It's a gimmick build that apparently got popular here from a reddit post talking about some guys in Korea who were trying it out.
"Should squishy assassins be encouraged to build damage instead of stacking health and armor?"
They already are. Assassins have plenty of tools that serve to effectively deliver the damage that they build.
"At this point I've got to ask if anyone could be an effective tank if assassins can get away with stacking health and armor."
No, they aren't for the same reasons. Tanks have great synergy with building defensive items and doing so increases their effectiveness while conversely, champions like Akali have no synergy with tank items. No matter the tank build, assassins will never be as effective at being a tank as a "tank champion".
The shorthand name for this build fad, "Tank Akali", is a bit misleading. People still play Akali offensively with it. What the idea is, is that by building full tank, it mitigates Akali's poor survivability and she can stay alive longer when she dives in with no escape. How it works is that it takes advantage of Akali's stickiness and low cool-down E and new energy restoration so that she can stay on top of enemies and spam E until the enemy falls over from E's base damages and Sunfire.
So..."Why are people playing Akali building her as a tank?" Because desperate times call for desperate measures. Or to say it with less idiom and more actual usefulness:
Because Akali is just that bad. Akali has not been in a good place for quite a time now. Even with this supposedly OP build, you watch a tank akali play and all you see is a champion who, as they fed as they are, should not have nearly that much trouble taking down just one squishy target. Gimmick builds, builds where you don't even build damage on damage dealing champions being the most common reason a champion is even picked is a pretty ominous sign. But that's the state where Akali is.