I think the main trick is that they set out to make the best and most impressive movie(s) they could with every tool available -- practical effects, old-school camera angle tricks to make the hobbits look small, hordes of extras and well-crafted props, as well as groundbreaking CGI.
Same with Jurassic Park, come to think about it -- there's famously more animatronic dinosaurs in that movie than CGI.
As opposed to relying on one shiny new tool to take care of everything. I think with The Hobbit they got over-enamoured with the notion that you can do anything with CGI.
More recently, Andor is a good example with its mix of CGI and massive sets; The Mandalorian is a bad example with its over-reliance on the "Volume" LED stage.