One obvious problem that I see with this approach is that it will break if there is any change in the storage format.
With client-server architecture, the server code owns the data format, while in this storage-level remote access case, you have to ensure that all of your clients are updated simultaneously. Depending on your architecture it might or might not be feasible.
For the typical uses for this, you'd tend to serve up a version of Sqlite compiled to wasm or JS to the frontend, so you can be sure it's the same one. Sqlite's storage format is also unusually stable:
It's better to ensure 100% compatibility with the data format so the new server versions can read the old format without conversions. For example, in ClickHouse, you can install the latest version over a version from 7 years ago, and it will work just fine with the old MergeTree tables.
With client-server architecture, the server code owns the data format, while in this storage-level remote access case, you have to ensure that all of your clients are updated simultaneously. Depending on your architecture it might or might not be feasible.