The main argument against SQLite is likely the cost of adding an effectively non-optional dependency. In particular, while SQLite is commonly available on Linux distributions, things are a bit harder on Windows/Wine. The implication would likely be adding SQLite as a bundled library to Wine (as well as CrossOver, but we're not necessarily terribly concerned about CrossOver here), so it may be worth getting @julliard's views on that beforehand.
SQLite is shipped with Windows as winsqlite3.dll, so it will be added to Wine sooner or later.