For example, we know the Pattern might make an opponent t'a'veren in order to counter an existing t'a'veren, implying that the Pattern operates on a broader basis than "must supply Dragon with convenient female lover/sidekick".

I think the main argument against the Pattern arranging for a mate is that all of Rand's most significant help and lessons came from women other than Elayne, Min or Aviendha.

I just think that if you applied the chain of reasoning you employ here to the series overall, it all becomes a mundane mess of things the Pattern programmed for, when it seems to me that the Pattern operates on a macro level, with specifics on the micro level coming about because of t'a'veren chance and the act of living your life out.