Why does extreme makeover help wounded soldiers, but government does nothing?

The basis of your question is incorrect. The government - through the Veteran's Administration - provides a great amount of services and grants to disabled veterans.

The biggest issue here is that this is done quietly and as part of their normal everyday business.

The TV show you mentioned simply made it appear that there was no assistance available because they wanted to make themselves look good and make a bogus political statement.

First of all, who told you that the Government does nothing? Also don't forget that the Government is "we the people". There is nothing stopping you or any one else from donating to a Veterans group, volunteering your time, etc... For example; my family donates to the Veterans Administration every year. As for the television show, it makes them and the people who watch feel good for the things that they do for Vets, this is definitely a good thing for the people who need it, there are also benifits for the contractors and companies who participate, it is good "public relations" and usually tax breaks (another way Government helps), etc... good for their business, all parties benifit.

Extreme Makeover is produced to entertain you. What the person helped gets is a part of the costs of production.

The government is doing something. Go visit your local V.A. hospital and then get back to us. How many wounded soldiers is Extreme Makeover helping -- tens of thousands? Don't think so. Again, go visit your local V.A. hospital and see for yourself.

it is called paperwork.

this can also be said for New Orleans. there is so much paperwork people have to file to build a house that 9 out of 10 people fail just to pall the written part of the work. while you have these celebrities (in your case extreme makeover) who can put up housing for people without filling out the paperwork.