What if Tywin had hired the Golden Company instead? He could afford them, they would be better in the field than the Brave Companions and at 10 000 professional fighters he may not have even needed to field Jaime. Harrenhall may have gone differently, why didn’t he? Or even literally any other company than the ones with the worst reputation? -A

Well, at the time the Golden Company was under contract with Myr and the only thing that can get them to break contract is the grand scheme to get their lands back. Also, given that Tywin fought against them in the War of Ninepenny Kings, he’s probably not on their most valued customer plan. 

In fact, Tywin’s failure to recruit significant numbers of mercenaries (the Bloody Mummers are both small and have a bad reputation even among mercenaries) in the War of Five Kings is a bit odd. It’s mostly a logistical mistake by GRRM – he admits that he forgot about the mercenary company who turned cloak after the Camps, for example. But my headcanon/No Prize explanation is that Tywin has a reputation for keeping mercenary costs down by using them as arrow fodder, so more discerning mercenaries avoid working for him.