The models themselves would be standardized and the weights and everything should be identical between browsers. They’d be standard and ‘web-safe’ like CSS colors or fonts. Probably would help to give them really boring/unbranded names too. These would work identically across browsers and web developers can rely on them existing on modern setups.
If you want more models, you could install them as a user or your browser could ship them or the web developers could bundle them through a CDN (and another standard for shared big files across domains would probably be needed)