The presses we have here has no issue with printing black. We run into prolbems sometimes when our chemical and plates are not so good.
If you want a rich black i suggest that you use C100 M100 Y100 K100.
Can't get darker than that.
It also depends on the press and pressman....he gotta get perfect registration.
There's another tip: some printing bureaus when they want to make a black in all its fullness, apply a pad (under black) about 30% Cyan . (offset printing system)