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For your problem is is enough to feed one output belt into one splitter and then merge those two outputs by sideloading on to another belt.
I tend to lane-balance when supplying onto, or feeding items off the main bus. Much easier to lane-balance 1 or 2 belts at a time than try to do the same on the main bus [for 4 to 16 belts].
Here are 2 designs that I use frequently [found online]:
http://steamcommunity.com/sharedfiles/filedetails/?id=956644588
Inserters prefer to take from the far side of a belt, but they'll take from the near side if the far side is empty. This tends to result in the two sides becoming unbalanced, but only when there's excess supply.
Changing the setup so that the sides are balanced would just result in a different set of assemblers being idle, i.e. those at the "downstream" end of the row would be idle rather than those on one side.
http://steamcommunity.com/sharedfiles/filedetails/?id=863231453
When one lane fills up it sends its contents down the empty lane.
Belt balancers a good when trying to send equal amounts of stuff down two or more lanes.
https://wiki.factorio.com/Balancers#Input_Unbalanced.2C_Output_Balanced
In this regard, we maybe will never know if the behaviour was intended or if it was created accidently and just left^^. Nevertheless I find it strange to look at whenever I see setups which use underground entries like that. The animation of the running belt, and that the belt entities don't join, just gives me the uncanny valley feeling.
http://steamcommunity.com/sharedfiles/filedetails/?id=947052904
both of these are good replacements for the 'classic' single splitter balancer.
http://steamcommunity.com/sharedfiles/filedetails/?id=959394629
The left site works only with more items on the left side of the belt. The right side work with items on both sides of the belt.
The OP was looking for something which balances the input, so that an equal number of items are taken from each side of the input belt even if items are only being taken from one side of the output belt.
But balancing the input side rarely matters in practice (and probably doesn't in this case). It's usually an artefact of excess production capacity (inserters prefer to take from the far side of a belt, but will take from the near side if there is nothing on the far side).
The first thing to do when fixing a problem is to check that you do actually have a problem, i.e. confirm that something somewhere is idle because it doesn't have enough ingredients. And if that is the case, the second thing to do is to determine whether the lack of ingredients is because you don't have the resources, or because you have them but can't transport them fast enough; those two cases have entirely different solutions.
example[forums.factorio.com]
On the other hand I have a 8 belt balancer, which "consumes" the items of the input side evenly, at the start of my main bus lanes where I unload the trains. This prevents that trains have to wait because they are unloaded unevenly. There you need a balancer like the one on the left.