Why active analog summer (adder) over passive summer exactly?
The concern about backfeeding/crosstalk only matters if:


The source(s) in question have enough output impedance to detect the unwanted signal
The signal splits off from the source(s) and goes somewhere else in addition to the summer


If either of those is false, then you don't care about backfeeding/crosstalk.



If you don't care as defined above, and you want an average voltage, then the passive adder is usually the better solution.  If you do care, or if you actually want to add and not average, then you need active.

The reason you need active to actually add signals is because the result could easily be higher than all of the inputs individually.  Since you can't get that signal swing from the inputs, it has to come from somewhere else, like a power supply.  That's pretty much active by definition.  You could feed a passive averager into an amplifier, but that's two separate modules that retain all of their own properties, both good and bad.

You might know this, but it's not clear from your question: The output from an active adder is negative, or inverted.  A positive sum is presented as a negative voltage and vice-versa.  This is how KCL and KVL still work.  If you really want a non-inverting summer, then you need to invert all the inputs (sometimes easier) or invert the output as a separate inverting amplifier/summer with one input.



It often helps my understanding of a particular concept to think of something I already know as a special case of what I'm trying to understand.  In this case, a voltage divider can be thought of as a passive averager between the signal and ground.  Adjusting the divider ratio and translating that back into a passive summer should show you how to make a weighted average.