Note: Voice

I would regard active and passive sentences as existing independently on their own without considering them as forms realized through conversion from some corresponding basic forms. This is because some things are best said in the active form while some others are best said in the passive form, of course, depending on the context, and even when most sentences with transitive verbs can be converted from the active voice to the passive voice and vice versa (there are some transitive verbs taking objoids that don't have acceptable passive correlates as subjects), there is more often than not a form (either active or passive) more preferable or appropriate to a particular semantic or stylistic context.

While children are necessarily taught active and passive forms and their conversions, I think it is important to tell them that active and passive expressions foreground and background things differently, and this has important impact on the meaning conveyed. This means that if one speaks or write English with its sensibility, then one knows the right structure appropriate to the context--either active or passive, not any.

My argument is supported by the example sentence provided in the original post:

(1) He was filled with sorrow at his father's death.

"[W]as filled with sorrow" feels so more like a state (a mental/emotional one) than an action that I would not regard this structure as an equivalent of "A + be + V-en (+ by + B)." This sentence (let's call it passive sentence) does not have what Allerton (1982) terms "perject"--the grammatical passive equivalent of the active subject (which some unsatisfactorily call "by-phrase") when the source of his sorrow is clearly there. The first important step of transforming a passive sentence into an active sentence is to bring the "perject" in the passive sentence (you've to supply it based on your interpretation of the sentence if the perject is absent though in most cases the perject is obvious from the context) to the start of the active sentence as its grammatical subject. But, in the absence of a "grammatical" perject in our current case, we are left with no option if we have to transform the sentence into an active one without making any change to its stylistic or idiomatic elements.

Yes, we know the cause of his "sorrow" and it his his father's death. While it is a perfect sentence in its own right, the second passive form of the original sentence (1) (above) proposed in the original post

(2) His father's death filled him with sorrow.

is not actually an active equivalent. If we do not make any change to the sentence's idiomatic or stylistic aspect, we have a prepositional phrase "at his father's death" which cannot function as a subject. While we can move "his father's death" to the active subject's position, we leave out "at" which (together with "his father's death) carried an idiomatic weight (and the active form does not account for this at all), and strictly speaking "his father's death" is not the grammatical agent of his sorrow, though we can understand so semantically, but this depends again on subjective interpretation or understanding of the thing. Leaving out "at" is critical here.

While it is also a reasonably good active sentence in its own right, the first active form of this sentence proposed in the original post

(3) Sorrow filled him at his father's death.

is also not actually an active equivalent for the same reason I have pointed out in the preceding paragraph--it leaves out the idiomatic element "with" and the active sentence does not account for this.

I think "be filled with" here is quite idiomatic and feels like an emotional state or state of the mind rather than an action. I don't think this usage of "be filled with" will have an exact passive equivalent, while sentences like (2) and (3) can stand perfectly well as active sentences in their own right.