Depends, a true republic is a far better environment for capitalism, and for freedom, but the US has been sliding away from its republic roots for quite some time as democracy pushes its way in, (democracy doesn't appear anywhere in either the Constitution or bill of rights). Republics have been given a bad name since they are used in monikers for totalitarian states such as Democratic Republic of Korea, Democratic Republic of Congo, People's Republic of China, none are either democratic or republics by any stretch, they are just euphemisms concocted by despots in an attempt to ligitimize their regeimes.
A true republic has laws for and by the people written in a constitution, like a basic play book, that can't be overwritten easily. The US has been whittling away at contitutional rights for years. We are not a republic and our rights disappear with the stoke of a pen, depending on the current zeitgeist, very democratically of course.
There are certainly things that should be publicly owned, highways, waterways, essential services such as policing and so on. But when it comes to businesses they always seem to end up as the playthings of the government in power, no matter their political stripe. I see the point where government has to provide a public service where it is unfeasable for private enterprise. But I have also seen where government sevices grew to where they actually compete with private enterprise. There comes a point where public services should be privatized, but competition has to not only be allowed but encouraged. My phone bills were cut by 3/4 once competition was extablished. Competition for power generation and distribution out here is not only discouraged, but in most cases not even allowed, and my power bills have more than doubled since the crown corp. was privatized, a case where free enterprise is allowed to run amok.
Government has a role to play, but it never seems to stay in one place long enough. The swings are often wide and erratic, either too restrictive and choking business, or too liberal, allowing greed and chicanery to rule.