The core issue is that the frequency of the details of your mesh is higher than your screen resolution. Following this we can either increase the screen resolution or do some work on the object being rendered to lower the frequency of the details.
I think that Nanite from Unreal Engine can solve this issue as it is basically an automatic continuous LoD system. But no other engine that I know of replicated the goodness of Nanite so that’s why the LoD solution is the most realistic in your use case. (on the web we don’t have Mesh Shaders so no Nanite for now it seems Meshlet for babylonjs? - #8 by roland)
The LoD is only one solution to this issue, but it is the simplest. You could also use a normal map and decrease the normal perturbation with distance so that only low frequency details are retained from afar.
More advanced solutions could also use some smoothing function in normal space before the lighting pass, again to reduce high frequency details.
The laws of physics are not always on our side 