Beauty is subjective and the development of taste is path-dependent. A thing can be beautiful because it evokes features that make a designar successful for functional reasons in historical media.
In the case of many of these structures, their physical form is a reflection of some spiritual aspect. They're basically religious icons. Their design may be carried forward in part just because not doing so would be disrespectful on a spiritual level, or because they remind people of something. But they're not all the same.
There are probably thousands of different torii gates with slightly different designs. Some show an extended nuki with kusabi wedges, a modified mortise and tenon style joinery. But many torii gates don't feature these. Nuki joints are actually widely used as ornamental carpentry, and can be found in several non-wooden objects.
The construction of most torii, regardless of their material, seems to be about aesthetics (and honoring whoever paid to put it up) before the rest.
If you want maximum accomplishment with a material, check out their multi story pagodas that use a massive wooden beam in the middle. It acts as a mass damper and prevents the different floors from sliding off the building during an earthquake, as they aren't attached to each other. Hard to do that with stone! :)
I’m inclined to believe that, if the original masterful wood-crafters had instead began their professions with stone, that they would have created beautiful structures that fully explored the capabilities of stone, and that their contributions to architecture may have looked a little different, but no less aesthetic.
So, assuming the will of the original craftsmen was to simply make the most aesthetic structures that their materials would allow (and maybe I’m wrong about that), would it be paying homage to them by making stone copies of their wooden accomplishments while working in a new medium with different characteristics, or would it be paying homage to them by continuing their pursuit and fully exploring the capabilities of stone, as the forefathers had done with wood?
That’s a question with no right answer... but I personally believe that homage is not to copy one’s output, but to copy one’s input.. To seek what they sought. To do as they would have done if they had stone instead of wood.