Europe is not densely populated. There is plenty of empty space, they just have decided to place rules on how that space is used.
The US east of the Mississippi and the far west coast has similar (lower, but not by much) population density. However there is a lot of space in Alaska and west of the Mississippi that almost nobody lives in and that brings down the density measures.
Thing is, we need to find out ways to remove, reduce and recycle plastics as soon as possible. The US may have enough place to place landfills without impacting anyone, but densely settled Europe does not - we're having the requirement that landfills can only take up 10% of residential waste by 2035, the rest has to be either burned or recycled by then. And for that, we need technology to actually recycle the plastic waste to be ready at industrial scale, so we need to focus on that right now. Sorting trash, separating modern multi layer plastics (sometimes a dozen layers of different materials!), recovering polymer source compounds, a lot of that is still open topics that need to be researched.
Additionally, landfills are already bad for the environment - Grady points out the issue in his video indirectly: the birds eat the food waste from all the packaging and end up distributing (micro)plastic waste across the environment surrounding the landfills, which then ends up in the groundwater and surface water bodies. Also the birds pick up and distribute pathogens from the decomposing waste.
Side note: we also need plastics recycling to reduce our dependency on fresh oil products used to manufacture them. Again, the US has it a bit easier due to self-sufficient domestic oil production, but Europe does not.
[1] https://www.europarl.europa.eu/pdfs/news/expert/2018/4/story...