"Rolling the version periodically" is probably quite problematic for browsers. Kind of a key point of the web is that stuff if at all possible keeps working. Breaking changes like that are hard.
Even if the spec just listed occasional version and the webpage could choose which one; that means a potentially tricky maintenance burden on browser to support old versions of a potentially no longer supported sqlite, and each version is another megabyte.
Why not then just choose this solution, and let each website pick its own poison?
If the concern is the repeated downloads of common resources, well, we've accepted that for other CDN's too, and a solution for shared caching of common dependencies would in any case be more valuable than merely for sqlite.
The current approach seems better than a browser-provided version.