The Halacha generally is, that before doing mitzvos we recite a bracha. However, before doing something to prevent or remove a danger we do not recite a bracha (for example mayim achronim). Therefore the bracha of al netilas yadayim is only said because of the reasons that we are like a fresh new creation doing Avodas Hashem and because we need to be clean for davening, but not because of the ruach hatumah.

The accepted minhag is that the best time to recite the beracha of al nitilas yadayim is before davening together with the other morning berachos, as we are expressing our thanks to Hashem for our renewed existence, and giving us new opportunities to serve him. Those that have the minhag to recite the bracha soon after washing, should be careful not to recite it while needing to use the restroom or while not dressed properly.  One who forgot to recite this bracha before davening, can no longer recite it after.