It's price is not that high - 300 more than liandri's - for an active nuke, chase/kite potential, dueling power, sustain, and ad- so even enemies stacking multiple mr items against you still take damage from something other than your ult. Also, that ad buffs the dft damage at a much higher rate than ap does. Thus - it gives you more magic damage on-hit.
Deadman's is great for engaging and that's about it. Once you get hit or hit someone, it loses the movespeed bonus which must be rebuilt - which can't be easily done during a fight. Generally, cho has no problem getting into a fight - sticking to a target if you can't 1-shot them is another story.
Ninja tabi is nice - vs aa ad enemies. But it alone is not enough and stoneplate without other true resistance items mean's little more than 4 sec of pseudo-tankiness. And then there's all those ad casters out there who kinda ignore a lot of tabi's resistances. Darius doesn't care all that much, kayn - especially darkin kayn - will just cc you, screw up all your combo's, dance around most of your damage, and probably utterly delete you. I mean, your ap cho build could be OK in some cases, but you will be as durable as an orianna in a teamfight and completely reliant on kills to keep yourself healthy. You are also much more reliant on hitting your q and w from range - rather than having the option to close to melee, land e, and then have easy q and w setup.
Also, I've played variations of the build I suggest and pretty much have found success vs many different enemies. At the least holding my own without having to hug tower in matchups where traditional tank cho would be bullied and forced to play very passive. Ad destroying enemies where you would normally go even. This in gold elo. So, the build definitely works to at least that level. And yeah, some of the stuff like gunblade sounds really weird until you try it. It's like I used to go hextech revolver (when it had spell vamp) into thornmail on morde toplane (before rework) and regularly 1v2 get double kills vs enemy double buff jungler and ad toplaner - with them both being level 6 going into the fight. Nobody built thornmail on morde - but I did and boy did it make life hell for enemies. They literally couldn't fight back. Gunblade cho is kinda like that - you never know until you try it.