The downside of that is that application developers would have to use the minimum supported version of SQLite.
If every site embeds their own version, the application developers can choose their own version that runs the same across every browser. Or even compile it themselves if they want, so they can use extensions. The download size is unfortunate but remember - unlike javascript, wasm bytecode loads almost instantly. Having a 250k wasm module is more like having a 250k image on your site than 250k of javascript. (Though it might still affect time-to-interactive depending on how the site is built)
If every site embeds their own version, the application developers can choose their own version that runs the same across every browser. Or even compile it themselves if they want, so they can use extensions. The download size is unfortunate but remember - unlike javascript, wasm bytecode loads almost instantly. Having a 250k wasm module is more like having a 250k image on your site than 250k of javascript. (Though it might still affect time-to-interactive depending on how the site is built)