Weird stat building on kayle.
So i'm fairly new (bronze 3) and I've recently picked up kayle. Experimenting with a few builds made me curious and I went into the training practice tool thing. I was surprised to find that the most effective builds, based on damage at least were ones where I build full attack speed and crit. Now this is weird to me as none of the builds I saw of kayle online have had crit or max attack speed. Furthermore, none of the builds I saw online built tank so it's not like they sacrifice as or crit for tankiness.
So in short, why can I not build weird stats on kayle/why isn't it viable? Example would be: Phantom dancer, statikk shiv, runaans, 2 nashors and a rabadon.
Is there a more effective build other than those found online? I'm in love with attack speed so I pretty much want any build I make to have 2.5 AS, is there any way to do that and still have kayle do a lot of damage?
Any help is appreciated.

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and
have passives named "lifeline." you can only proc one of the passives at any given time, so buying both those items together is generally a bad idea.
after
no spell blade.