|The stupid question is the question not asked|
Is there a generalized solution that minimizes error if the closed list is converted to an infinite list?
Given the nature of the input, how are you seeking to convert that to a specification of an infinite list?
What I mean to say is that there is a fundamental conflict between "uniform distribution" and a variable length list.
Using your example input, until the list reaches a length of 10, adding an 'e' will mean that 'e's are over represented; but waiting until the 10th take in order to add the 'e's, means that if the list stops there, the 'e's aren't "uniformly distributed". At least in as much as your post implies uniform distribution whereby intuitively, a single letter, should appear somewhere close to the middle of the list. There is no way to maintain that definition of "uniform distribution" whilst generating a list one element at a time. (Not even if you knew the final target length up front.) You would -- and, at best, could only -- achieve that definition of uniform distribution every mod(M: where M == sum(f0n)) elements.
If that is acceptable, you might generate a single natural length, uniformly distributed list internally, and then return that one element at a time, cyclically. The distribution will only be perfect every M takes, but it will never be grossly wrong, which meets the "minimizes error" requirement.
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