The problem is no one is ever going to put in the work and prep production effort that Jackson and his team did. It could be made better and more modern, but will it in our current environment? No, all the practical effects would be replaced by CGI, all the armor and costumes for the tons of extras would just be CGI, the extras themselves would be CGI, and it probably would be packed with meta commentary and jokes. Just look at The Hobbit compared to Lord of the Rings. It doesn't work without all the effort and pre-production, and I don't think we're getting a studio to ever make that bet again. It was pure luck we got it the first time.

Some of the green screen shots could definitely use updating

It still looks better than The Hobbit though.

The CGI is still a bit dated (although somehow The Flash topped that), but there's far less compositing of solo actors in green rooms, due to forced perspective.

Man, hard disagree. Some of the CGI hasn't aged especially well but those movies are technical marvels, the likes of which will never happen again because nobody will ever have the passion for the project Peter Jackson did.

I think part of it is that movies are edited differently now. We've become used to much faster pacing, much denser storytelling and sweeping drone shots of everything, so older movies generally feel a bit lame now