An alternative could be to allow loading the contents into 2 empty memory elements in case there are two of them currently available. Would require the fluid storage to have 2 slots as well.
With the ability to convert to 2 memory units you can then continue to split one (or both) into smaller and smaller fractions and then recombine the ones you want (like binary numbers) to get any sized fraction in logarithmic time without having to send actual items on belts.
We can already merge memory elements (send 2 memory elements with data and then 1 empty into storage unit) and read the contents of a memory unit (send in memory unit, read with circuit network and then send in new empty memory to repackage now that you know the contents and count). So by simple balanced save into 2 empty memory units all the tools necessary to redirect items by count are there.
Right now if I have 1 trillion items in a memory element/storage unit there's no way to quickly get 100 billion items to each of my 10 stations. The only way to get the items out is by extracting them individually with loaders/bots/belts from a single storage unit and wait hours and hours to extract them at a max rate of like 25 stacks per second. Since a big late game base can mine resources from ore fields faster than that the items are kind of trapped and regardless of how many items you have in a memory element you are better off just throwing it away(!) and mine new resources and store those in smaller quantities for transport and distribution.
It also means storage units are bad for actually storing items since the extraction rate is so low for a big enough base. It's better to convert to memory elements (with maybe a few minutes worth of extraction stored per element) and store the elements with data in chests. So the storage units are only good if you use many of them and don't utilize their capacity, or only use them for compressing down to memory elements and never store things in them. If you use many of them to store things then whats the point of infinite storage capacity? And their space footprint is large and they require energy, 1 chest is a single tile and can store 48 memory elements so they can store much more than a 3x3 entity that can only store 1 memory element (and chest still have 432 times higher extraction speed since the elements can be distributed to many storage units for fast extraction).
Basically, without my suggestion the memory storage is a big throughput bottleneck and should not be used for storage of large quantities (many millions). The capacity to store infinity, the infinite input throughput to one storage unit (with merging) and fixed small output throughput is quite a sad combo.
With splitting the circuitry to split off and merge repeatedly could be an interesting puzzle. OP's original suggestion would work as well but would be throughput limited to what a circuit network can give unless we can get signals in and out in scientific notation (multiplier, base and exponent). So with duodecillion items splitting in half 30 times is quicker. And it would not be unreasonable at that stage to use up a hundred memory elements to split down to memory elements that are small enough (millions) to be read with circuit network and merge back up based on amount of splits required so scientific notation isn't even necessary to handle less than ~2^(2^31) items (number of splits required is logarithmic to size of storage so we can count the splits used to get down to millions and by that get the exponent).
