@dr0ptp4kt: That's an nice idea! Hope you keep us up to date about the state. Thank you.
I guess you mean their LoD implementation, or you might also ask for their .obj sanitization?

In this example https://sketchfab.com/models/fa94d763e89d437e84c31d5110a3c6a4 you might see that the file is loaded step by step. That's not the same as the requested feature, but might be of interest anyway (more in technological way as in an way to use in Wikipedia I guess). As the original, download-able file has nearly 200 MiB in size, there must still be an server-side LoD functionality.

@dr0ptp4kt: Oh I'm sorry, it seems that Sketchfab changed their UI. :-/
It's already up to ~1.5 years ago that I first engaged with this topic, I don't know when I last visited Sketchfab. In the past they served an option in their viewer showing several LoDs including file size and/or vertice/face count (can't remember exactly). Today they only left an "Texture" parameter with the only available option "HD" (or the only available for my, maybe my hardware is too old - if they are able to recognize this). Even not for files with 1 and 2 mio faces: https://sketchfab.com/models/00754d1a71b543d1ac6bb22a0f01b255 and https://sketchfab.com/models/6898d4c2514d4920960f2f85c2b162f9 for example.
(You might find more searching for 'photogrammetry' (-> https://sketchfab.com/search?q=photogrammetry&sort_by=-pertinence&type=models), my laptop tends to crash since a while on high load. ...)

@dr0ptp4kt: The LoD should and would be independent from the used filetype. The procedure would be the same as with images: The server needs to create an lower leveled/detailed, additional file. Sketchfab for example uses (or used) .obj files in that way.
By the way: Has somewhere been discussed which filetypes we are able to use and which not?

@Yurik: Thank you for this information, I was always thinking about how to solve this on server side. But are you sure this could handle WebGL features? (At least this is part of T54655.)

As mentioned in T63523 this also happens if the link is directly opened into a new tab/window or directly copied with the context menu.