Aaron Bertrand walks us through a case where filtered indexes become unhelpful:
Again, focusing on the areas highlighted in orange: the statement has a parameter @0 (previously it had @1) but, more importantly, the clustered index is scanned now instead of the filtered index. This has impacts throughout the plan, including how many rows are both estimated to be read and actually read in order to return those 11 rows. You can see a much higher I/O cost (about 22X), the predicate is now listed explicitly in the tooltip, and you can see warnings about residual I/O (which just means a lot more rows were read than necessary). The root operator still has the warning about the unmatched index, so at least the plan gives you some clue that a filtered index exists that might be useful if you change the parameterization setting for the database (or add OPTION (RECOMPILE) to the statement):
There are still ways to make filtered indexes work with forced parameterization, such as index hints, but Aaron does a great job explaining why something which seems like it should just work doesn’t always.