Well, you may be right in an ideologically pure world, but that world doesn't actually exist, and you should perhaps think about what is required by the real world. (Further, government has a legitimate role in supporting the economy when the failures that you say Capitalism needs overcome Capitalism's ability to recover. Read up on the Great Depression, and remember that Capitalism's self recovery mechanisms were too feeble to get us out of the Depression. What got us out was the grand daddy of all government stimulus programs, WWII, after which the US was deeper in debt, as a percentage of post-war GDP, than it is today. We paid our way out of that one by raising taxes which coincided with a period of great American prosperity. Kind of knocks the wind out of the "lower taxes to create jobs" sails, dontcha know.)
To return to the topic at hand, to keep America strong and competitive from a strategic point of view. Sure, most companies that can't justify themselves should and are allowed to fail, but we need some strategic capabilities that we can't allow ourselves to lose. There have been many examples where the government had stepped in to do things, including propping up companies, that were required for the strategic advancement of the countries.
I'll start with the building of the transcontinental railroad in the 1860's, which was paid for by granting 10-square-mile alternating sections along the right of way through the great plains and elsewhere that the railroad companies then sold to farmers who would benefit from having a rail road close by to get their goods to market. The government then proceeded to essentially rebuild these railroads at taxpayer expense for WWI and WWII, to the benefit of the private railroad companies, because of national strategic need. The railroads certainly weren't and couldn't make the necessary investments. Good thing the government did this, or you might have learned German in high school instead of French or Spanish. For background, read "Hear that Lonesome Whistle Blow" by Dee Brown.
There are other examples, but no room and little time to write about them.