The water and soil pollution from a landfill is predominantly caused by biodegradable waste. Hard plastics aren't a big contributor because they're stable for a hundred years.
"This is future humanity's problem, if there ever is one" is not a great argument though. Eventually it destabilized, and 400 years from now all the plastic we've put in the grounds in the last few decades will "suddenly" all create a whole new problem.
Yes, but climate change is definitely going to cause problems in far less than 400 years, and landfill soil pollution is highly regional problem, not a global problem.