Why does that make the "ends drives the means" method better than all other strategic methods?
It avoids the Alice In Wonderland situation. If you don't know where you are going anyroad will take you there.

Why should we only have one strategic method?
Not sure I understand the question but it is a single process that will produce multiple Strategic options, a very good thing IMO when you are dealing with those pesky Complex systems you talk about.

An example of a problem set where an "ends drives means" approach won't work:

http://www.armedforcesjournal.com/2009/12/4252237/
I have been following the Design debate on the Blog. IMO they are going down the road of EBO. They will end up with something so complicated that it will end up being useless.

The current Libya situation is one where the drive for action precludes taking the time to form concensus on the desired end state, so we are forced to use "trial and error" ("muddling thorugh" in the authors terms). The author argues this is the normal state of things, not the exception.
That is not a desription of a wicked problem, it is a description of a mistake IMO.

Should Adm Mullen has stuck to his guns when he said that establishing a no fly-zone over Libya was "too hard"?
No he should have said in his professional military opinion that a No Fly zone will not accomplish the mission. But if the political objective is to protect the population he would do his sworn duty and create a Strategy to accomplish that mission and present it before him when completed.

What should his response have been to being dressed down by Sen McCain something to the effect of "We spend 700B$ a year on the military and it can't establish a no fly zone to ground a couple dozen POS aircraft over a tin pot third world dicator's third world country????"
The response should have been "Tell It To The Marines"

"I would be derelict in my duty, Senator, to engage in such an endeavor without a clear vision of a desired endstate."

I don't think so...
See all the above