Exactly. LOTR was a masterpiece in balancing CG and practical effects, they didn’t overuse CG. That didn’t mean they didn’t use it, it means that when practical was better, they used practical. When LOTR used CG, it was because it could not be done at the time with practical effects; you just can’t make someone look like Gollum without making their suit and prosthetics impossible to act in. This was before motion capture, they had to animate Gollum BY HAND using Andy Serkis as a reference. Four tusked elephants with tiny people walking around on them aren’t exactly on sale, nor are fell beasts.
Isengard and Orthanc? Bigature (miniature but like, the size of a tennis court). Minas Tirith? Bigature. Helm’s Deep, the Black Gate, Barad-dur, Minas Morgul, Osgiliath, even elements of Lothlorien, Moria, and the Grey Havens? BIGATURES. Hobbits and Gandalf in one shot? Almost always tricks of perspective with, for example, a table set that was made in 3 pieces to move and make you think Tiny Elijah Wood™ was sitting at the same table as Giant Ian McKellan™, not greenscreen. They literally went so far as to make the Hobbits’ clothes (on the taller actors, not their little stunt doubles) with thicker thread to make their smallness look real.
Those statues, the Gates of Argonath? CG. The gorge and the boats? Real.
But the thing about the top example with the dog? They’re doing it because CG is less expensive because animal handlers have unions, while CG artists don’t and work in sweatshop conditions.