I don't use it at the moment but there is one remaining modern browser that does not support indexed_db, that being the embedded Safari web view on iOS. I suppose we can expect that indexed_db will appear there eventually but until it does web_sql remains the escape hatch. Eventually, if Apples never implement indexed_db support in embedded safari, I can imagine using web_sql. Although dart:js access to it is okay if web_sql disappears.
A further point to consider is that there is still quite a lot of variation in the quality and completeness of indexed_db implementations. I imagine that a demanding application that uses web sql may not be ready, or able, to change until indexed_db implementations improve. Not a Dart issue per se.