This is one of the greatest tricks socialist have every played, and anti-socialists have played into. The idea that any form of government action or ownership is "socialism" and thus originated with and represents them.True, but state ownership is technically social ownership, which is one of the core principles of Socialism. It just doesn't look like Socialism because it's such a tiny part of it in isolation; like taking a single Lego brick from someone else's project, and using it in your own.
In reality, that isn't the case in the least. Most functions of government, even the idea of governments owning the means of production, predate Marx. Hell, that core one, the idea that government owns the means of production, actually predates Marx by thousands of years, as it's a core component of the primary Bronze Age economic system known as the "Palace Economy". Writing as we know it literally developed in response to the demands of maintaining such an insane centralized system, and the Bronze Age collapse was, in part, amplified and caused by the failure of those centrally planned economies.
As for his ideal communist utopia? It's really just a repackaging of the Christian view of heaven. No wants, everyone free from labor, etc. Yeah, it's just the Christian ideal of heaven stripped of God and religion and claimed to be makeable on Earth.
No, the reason for the continual appeal of Communism is much more simple. It's not because it has "good ideas". Heck, I'm not even convinced Marxist histography is that useful, as it appears to reject what people say about their own actions and instead replace their motives with "Class Struggle" propaganda. Seriously, take a look at the massive and stark difference between the traditional historical understanding of the American Revolution and the Marxist understanding of it. Looking at economics and their role in history is hardly unique to Marxist histography, that's ALWAYS been a core part of looking at history; however, the emphasis on class struggle is quite ahistorical, as most people did not, and do not, see themselves primarily as members of an economic class, nor do all their actions conform to pursuing class interests.
Going back before I got distracted rejecting marxist history crap, the core appeal of Socialism is quite simple: it plays to people's Envy. Throughout history, and for the foreseeable future, there are people who have more than others, and there are numerous people who resent the rich for that. This envy, that resentment that others have more than you, is a core indicator of support for socialism and while compassion for the poor also does play a role, it is the combination of resentment and compassion that serves as the highest indicator.
Envy isn't going away, thus, the appeal of Socialism will never truly go away either.