The real reason to play the Cold Steel games first is because the translations for Zero/Ao aren't exactly up to par at this point; in fact they aren't even localized.
I keep seeing this suggested order for the "complete experience" even though Zero and Ao were released before CS. Did Falcom really intend for the players who played the games as they were released to not have a complete experience? Cold Steel and Cold Steel 2 spoil just as much about Zero and Ao, if not actually more.
While Ao does spoil three very important things, those are things that happen towards the end of each game. On the other hand, the Zero/Ao spoilers in Cold Steel are for the duration of the games, especially if you read the newspaper. Sure, they lack context, but when you're playing Zero and Ao you'll be able to easily piece together 1+1 and know exactly what the major event will be in almost every chapter. Another thing is that there are constant references to Zero/Ao in Cold Steel, even some minor returning characters from sidequests. That's not the case in Zero/Ao, since it released earlier.
Oh and last but not least, the spoilers for Cold Steel in Zero and Ao are intended spoilers. Falcom wouldn't want to diminish the experience of Cold Steel for people who played their previous games, and this is clearly evident considering how the major spoiler for CS in Ao is delivered: It's a completely unnecessary to the story of Ao comment that they could easily have not mentioned. Yet they chose to mention it.
I don't mean this as a rant, just tired of seeing people suggesting that the release order is the wrong order to play as if you want the complete experience. I also suggest playing at least Ao last, but only because it's not properly translated. When it is, definitely play Zero and Ao before Cold Steel. And I'm not trying to say either order to play the games in is bad. I just wouldn't say that you need to play Zero and Ao last for the complete experience.