I don't think the 80s nostalgia has much to do with a love for the violence or neoliberalism. Rather I think it gets focused on for three reasons.
First, it was the last decade without the internet and a number of electronic devices that have been blamed for modern alienation and loneliness.
Second, I think it's used as the poster child for the cultural dynamism of the late 20th century. The 20th century, and especially the latter half of the 20th century was very culturally dynamic, compared to the relative cultural stagnation of today. Since the culture of the 21st century is largely a child of the 90s, that makes the 80s the last 20th century decade to have a strong, marked difference from the culture of today. I think a part of the nostalgia is a desire for that much more dynamic popular culture environment.
I tried to make a thread on this before, but it immediately derailed and turned into bickering over whether or not 20th century culture was actually qualitatively better than than the culture of the 21st century. I made the mistake of trying to demonstrate how much the culture changed over the decades with rock music videos to show the differences between a single genre of music between the decades (vids related), and apparently a bunch of people have rock snobs that live in their heads rent free.
Lastly, the 80s was arguably the last "futurist" decade. There was still some futurism in the 90s, but the 80s really embodied the ethos. People who grew up in the 21st century might not even know just how much people in the 20th century believed
in the future. It was almost quasi-religious. The idea that society would continue to evolve and build up at an ever increasing rate, and your children would live a significantly better life than you would was basically social canon. And a lot of the styles and artistic movements were centered around embracing this coming new age. It's something that really doesn't exist anymore. And so, for people who can't see a future in their present, they often have to look back to the past, when people did believe in a future and looked towards the coming of the new age.