Well "Going private" doesn't mean anything. It can mean PE. It can mean "traditional" personal/family ownership (e.g. Musk with Twitter). It can also mean moving to a co-op model (theoretically I don't think anything stops a bankrupt publicly-traded company being bought by its workers). "Private" doesn't sit anywhere on the political spectrum; even Marxists can generally agree that co-operatives are in principle better than publicly-traded companies.

Unfortunately PE firms are usually the ones who win the bid when a company "goes private" because the PE business model is driven by speculation and leveraged buyouts, and (at least in the US) supported by advantageous tax rates. Even from a purely capitalist perspective it's an objective failure that harms the macro-economy. It's not even capitalism anymore; it's oligarchic.