Belt balancing is necessary when unloading trains, as otherwise uneven consumption can lead to some chests/wagons running out of resources but the train doesn't leave because other wagons are still full.
For mining outputs, it can also be nice to avoid the outpost getting slow/stuck (never able to fill a train) when ore runs out for the outer lanes of miners.
Anywhere else, balancers are unnecessary and just serve to obfuscate a lack of resources.
(But if you really want to play without any balancers at all, that's quite possible: the train problems can also be solved by letting trains leave on a schedule independent of cargo status. All remaining balancers, including those on mining outposts, can be replaced with priority splitters.)
> Belt balancing is necessary when unloading trains, as otherwise uneven consumption can lead to some chests/wagons running out of resources
Not in general, actually. If you standardize on N-wagon trains, and build assemblers (et al) in groups of N, each assembler can take inputs from one wagon in lockstep with N-1 other assemblers taking from the N-1 other wagons, and since productivity is deterministic[0], they'll also produce outputs in lockstep.
This means that as long as all your input trains are balanced (they should be, by being completely full), all your output trains will also be balanced. Science labs are same as any other machine, just without output, and trains feeding a logistics network can unload into active provider chests.
In practice I pretty much only use balancers for a: mining outposts, or b: random kludges, at least when and if I'm using trains as my main transport mechanism.
0: Ask me about quality once 2.0 drops; for now I just special-case uranium processing.
Strictly speaking it hardly ever actually matters, but yeah I usually use N=8 just so I don't have to care.
It should definitely be a even number so that if your machine layout doesn't work modulo 7 tiles (=1 wagon-length), you can group up pairs and use 14 tiles, but it might be helpful to use N=6 or N=12, and sometimes build modulo 21 tiles. (I haven't needed/tryed that so far, so I can't comment on how well it works.)
For mining outputs, it can also be nice to avoid the outpost getting slow/stuck (never able to fill a train) when ore runs out for the outer lanes of miners.
Anywhere else, balancers are unnecessary and just serve to obfuscate a lack of resources.
(But if you really want to play without any balancers at all, that's quite possible: the train problems can also be solved by letting trains leave on a schedule independent of cargo status. All remaining balancers, including those on mining outposts, can be replaced with priority splitters.)