I can't speak for other engines but at least SQL Server and Oracle will eliminate unnecessary joins for inlined table-valued functions, e.g.:

create function thing (a, b) returns table as select * from table_1 left join table_2 on ...

select (only cols from table 1) from thing(a, b)

..and table_2 is not accessed

predicates from the topmost query will be pushed down to the function's query as well so the functions performance is generally equivalent to the adhoc version.

on the whole I find this strategy to be very effective at reducing the complexity of adhoc queries without performance penalties. in the case of indexed views it can greatly improve performance.

Worse, someone is using the view (that joins several tables) in a join to get one extra field, which would be a simple single join -- they just didn't bother to check where it came from because 95% of the time that view gets used, and no one questions it. I've seen it happen more than once.

Why would that be a problem?

Unless you're fetching all the unneeded fields as well, in any decent DBMS both approaches would result in the exact same execution plan with the exact same performance, the unneeded parts/joins of the view wouldn't be executed.