Note: This answer was based on the example sentence f. originally having a different word order. The question itself has since been updated.
Google Books NGram Viewer, when comparing taken good care of and good care was taken of, at least suggests that f., is the far more common phrasing in print.
If the modifier from good to great, the difference becomes far less pronounced.
But though the gap between the two is much smaller with great, the X care was taken form remains at the same low level of occurrence.
If I replace good with enough, only taken enough care of appears—enough care was taken of doesn't have enough hits to appear on the graph at all.
Finally, if I replace good with little, the reverse pattern is seen. With little, little enough care was taken of is actually the more common.
The general trend seems to be that taken X care of is more common than X care was taken of. However, that's not true of every modifying word. Still, it's not the case that good is the exception to the pattern; in fact, it seems to fit into the more common pattern.
Why some words change the commonness of the overall pattern, or even why the overall pattern exists, may be a matter of speculation.
My answer to the original version of the question.
Your use of the modifier in f. isn't in a normal position.
When you use such a modifier, it goes directly in front of what it modifies. I'll use good as an actual example.
We use good care, with the one word directly in front the other, and nothing intervening.
Therefore, you wouldn't normally see, as in the question:
f. ✘ They were good taken care of by me.
In fact, that's so unidiomatic as to be essentially ungrammatical.
Instead, you would say this:
f. ✔ They were taken good care of by me.
Compare that version to g:
g. ✔ Good care was taken of them by me.
With the corrected version of f., I'd say it's no longer obviously inferior to g.
