Over high latency links this would be virtually unusable. Why not just download the entire database into memory over XHR on page load? SQLite databases of pure data usually aren’t over 10MB in size.
This particular demo page actually makes queries against an almost 700 MB large (fills one CD!) SQLite database. Because the amount of data read is almost negligible (few hundred kB), performance is limited by latency (as you say). However, high-latency links also tend to be slower, so downloading the entire database a-priori would almost always be much slower.
For example, on a 1 megabit/s link with 300 ms RTT, one example would take about 2 seconds for the data transfer itself while spending another 3 seconds or so on waiting. Downloading the entire file would take around an hour and a half.
For your 10 MB database, transferring it as a whole would take 80 seconds. Assuming this solution instead needs to read e.g. 250 kB (taking 2 seconds to transfer), it could still bounce around 250 times to the database before those 10 MB are fully downloaded. (This would be a really odd query, since it would only read on average two pages per read request)
Right but that is an artificially created demo by the author to justify the solution being presented (no offense). The question is how common are ~GB large SQLite databases in the real world relative to databases that are ~MB large?
In my experience SQLite databases of millions of rows of raw tabular data tend to compress very well into dozens of megabytes. Indeed SQLite is often touted as a file format for applications.
SQLite is most interesting not when the database is small, but when there are very few writes and all you do is reading. You can also look at https://datasette.io/ and see how SQLite is perfect for representing a lot of datasets and querying them