Private industry should be in control in some aspects of trade and production, but not in others. Capitalism is a means to an end: SHARED prosperity, not just prosperity, and where it fails, government should play a role. Case in point, health care and child care are places where government should play more of a role. Your approach of "who controls industry and trade" is way too simple of a question.
See here’s the agenda. The same people are in power in each scenario. They’re the ones rigging it for themselves and in socialism they’d be able to rig it even more for themselves. Not the answer.
For example, I don't think the government should wield negotiating power for something like hair loss pills, but I do think it should be throwing its weight around for something like insulin. Does that make me a capitalist? Socialist? Communist?
If we're picking up on the slider analogy, a capitalism slider that's closer to socialism than corporatism would do way better in creating SHARED prosperity for people. Look at the Nordic countries. People say "we can't have what they have", but the only legit reason is racism. Not the size of the US or any of that other bullshyt that gets spit out.
At the very least, we need socialism where profit motives are in contrast with people's ability to, idk, not die or go completely bankrupt due to a temporary lapse in employment. Or to not have to have a herculean effort to turn your family's socioeconomic status around.
None of the benefits of capitalism that most human on this planet enjoy can actually enjoy get destroyed by having medicare for all, a single bloc negotiatior for drugs you need to stay alive, etc. We're literally talking about adjustments that would have some billionaires only able to make 20 generations of their family millionaires instead of 30, lead to smaller yachts, less private space flights, etc.