It's not luck, that's the point; cop is pretty strong and has a stun which drops your defenses even more. However, as shown in the clip, you can circumvent most of those by using talk options to enrage (blocks the stun skill) and fear (drops dex so hit%, damage dealt, evade% go down and damage received go up), and that with CHA 1. I used it on both fights. The hobo has extremely high dex, so no talk options work on him, making him invunerable. On the clip, I tried enrage, attack twice, fear, everything failed. I have no idea how the guy who answered right after my clip says hobo "can be killed pretty consistently by using a specific talk move then attacking" when it shows without a doubt you CANNOT use talk options with base stats on him. This is why both cop and nun could be a bit stronger and the hobo fucker should be less agile.
About the poison, as you said, it's a pain in the ass only at the very start - then it's pointless. That's why it should be sta% based, at least current sta%, so it would take longer to kill the entire sta bar. Ten days are enough to reach almost 600 stamina if you ignore yuna and simply run during the first loop, and after that the poison ticks are useless. However, the hobo isn't the only guy using poison. The psycho lady at beach also has one (which is worthless all the time), and especially the silent hunter at countryside, which is also flat damage. And this also causes a problem, because her poison is way, way stronger than anything else in the game; if you try to fight her with 1200 sta, her poison needs 15 ticks to destroy you with an average of ~80 flat damage, not counting the stun and extra attacks which can increase it even more. And, as usual, it becomes negligible after 50 days when you have 13k stamina. Now she's another stun machine to combo with the lumberjack lady/iron maiden in the hopes regular damage can do something (it won't most cases, you can dodge all stuns by defending).