I'm sure I've talked about this here before.
It's true that {da de broda be di} is equivalent to {da broda di de}, but it's not true that {broda be di} has different place structure than {broda}. It's just that the second place is already filled, so {de} takes the next unoccupied place. Meanwhile, {da fe de broda be di} is equivalent to {da broda de fe di}, so there are two sumti for the second place (possibly equivalent to {da broda de jo'u di} or something).
At least that's how it is now, I'm not sure whether you're talking about current Lojban or proposing new things.
I don't know if you could really call it "the way Lojban is now" because stuff like this is extremely rare. What I'm trying to do here is provide a comprehensive analysis of what happens on the selbri level when linked arguments are used. The conclusion that I reached is that {be} is a selbri operator much like {se} that will indeed *modify* the place structure. {broda} and {se broda} are indeed different selbri, even though one is clearly derived from the other. Similarly, {broda be ko'a} and {broda} are *different* selbri.
(I have put parentheses around the selbri in places where isolating it aids comprehension.)
With that said, it shouldn't be unusual that the place structures be different. Because using {be} drops a place from the structure, the other places should move forward. {ko'a ko'e (broda be fo'a)} is equivalent to {ko'a (broda be fo'a) ko'e} because we are allowed to move sumti from the head into the tail freely. The sumti that are linked directly into the sumti are invisible to the formal structure sumti. This becomes more obvious when we isolate the selbri and write this out in {me'au} notation. {me'au} is an experimental cmavo that allows function abstractions (i.e. {ka}-abstractions) to become selbri.
e.g. {mi do (me'au lo ka ce'u cinba ce'u)} -> {mi cinba do}
(Formally, {me'au} is of selma'o ME.)
Do demonstrate the effect of be operating on a selbri level, using me'au helps, such that {broda be ko'a} as a selbri is equivalent to {lo ka [ce'u] broda ko'a [ce'u] ...}
Therefore, {.i fo'a fo'e (broda be ko'a)} -> {.i fo'a fo'e (me'au lo ka ce'u broda ko'a ce'u)}
Using {fe} on the top level therefore has no effect, as it is operating on the formal place filling level and not the selbri-internal level, where {ko'a} resides in the example just above.
{.i fo'a fe fo'e (broda be ko'a)} -> {.i fo'a fe fo'e (me'au lo ka ce'u broda ko'a ce'u)} which is equivalent to {.i fo'a fo'e me'au lo ka ce'u broda ko'a ce'u}. The {fe} indeed has no effect of double-assigning a place, in this case. Another way of looking at it would be to say that using be moves the sumti directly into the selbri, which is outside the scope of top-level FA. Even if at this point it were still debatable, saying that it causes double assignment would be less productive, I think, as double assignment in general is unuseful. (I don't think it's entirely pointless; it's one solution to the problem of using {sei} and splitting quotes: {.i lu coi pendo li'u selsku lo verba fa lu .i do mo li'u})
.i mi'e la tsani mu'o