For sure - little c big T
About half our sim time is used for training - some of it LOFT, some specific exercises and much of it directed by the pilots. All of the time is aimed at development - whether it's training or proficiency.
If you spread the mandatory check items over twice as many checks, there are half as many to do each check
Many of our checks don't include engine failures, for instance, and are based around the line-oriented scenarios you describe, which I agree are invaluable - whether it's presented as LOFT or LOE doesn't really matter, if it's delivered properly.