The exposure which is measured in Lux.Sec is only intensity x duration. The sensitity isn't the exposure.
The bucket analogy is very useful for beginners just learning to set an exposure. It can get unwieldy though when we start talking about more advanced possibilities.
For example the bucket analogy suggests that "a single perfect camera exposure setting exists" where the bucket is full to the rim, no more, no less; when in reality for most negative films "there is a significant range of possible exposure settings" (EI's) that can be used to get excellent prints.
Part of this "perfect exposure" myth comes from Adams et al, in that they quantified perfect and people like firm right/wrong definitions. The problem is that the west coast school definition of perfect is based on a set of criteria (an artistic ideal) that doesn't necessarily matter to others. (Specifically sharp focus, typically small apertures, no visible grain, minimizing exposure time...) To those who shoot short DOF, who view grain as part of the expression, or who have camera shutters that top out at 1/400 or 1/100 and who purposefully use fast film mid-day, the calculus is very different.
The other problem that the bucket analogy has, is that it suggests to the person receiving the analogy that "everything in the bucket" (everything on the negative), will or should naturally straight print.