When we do so, it is illustrating how we rely upon Him for help, and proving our sincerity to Him, establishing that we recognise His infinite knowledge and wisdom. Islam is likened to being as a house, and in my estimation nothing cements that house together as well as putting our trust in Allah. I am surprised at the criticisms thrown at this du'a, and of its negligence. We are humans, powerless in this sphere of life, knowledgeable only enough to survive. Allah responds to the call of His servant when he asks for guidance, and we are after all seeking to do something in order to please Him.
Many wrong notions exist concerning istikharah.
Many Muslims will pray, read the du'a, and run to bed expecting to see a dream showing them their future wife, what her favourite colour is, and some other weird fantasy. That is not the purpose of this salaat. The results of an istikharah can take many forms. Basically, you go by your feelings, whether you now feel more favourable or not. Also, you may notice events have changed, either for or against you.