Should all branches of the military wear a US flag on their uniform?

Ok, I apologize in advance once again for bringing Civil Air Patrol into the mix, but an interesting and heated debate has arisen the last few days that might be relevant here.

-In 2007 CAP's national commander added the reverse american flag on the BDU uniform. This change was met with a lot of resistance, many people were not happy with the addition.

-A few days ago, CAP's new uniform manual began phasing the US flag out and once again, many people are upset, saying it's disrespectful to remove it from the uniform.

-Here's my opinion: The Army is the only branch that wears it, and CAP is not the Auxiliary of the Army. I read a few discussions about why most branches don't wear it and I agree. It is a work uniform and poses the risk of soiling or tearing the flag patch. I, as a Crew Chief understand this and would hate to have to replace it every time I spilled hydraulic fluid on it. The Army has it a little easier being their patches are Velcro so it can be easily replaced. I also heard by rumor that the Army was discussing removing the US flag as well. Is there any truth there or just rumor?

What are your opinions? Should all branches of the military wear a US flag on their uniform? Why do you support your opinion?