Whenever I look at online voting schemes, the idea of homomorphic encryption being a key concept, specially in the form of homomorphic tallying, appears to be universally accepted. The accepted answer for this question, for instance, suggests that it is one of the two most important technical approaches to online voting (the other one being mixnets).
The general approach for homomorphic tallying that I have found so far (supported on different additively homomorphic encryption schemes) is to define the tally as a single number, assigning some bits to the part of the tally corresponding to each voter. For instance, assuming that we have 4 voters and 3 candidates, the tally can be represented by the bit string ABCDEF, such that the candidate 1 has AB votes, the candidate 2 CD votes and the candidate 3 EF votes. In the general case, getting the values for each candidate given the integer representing the tally should be a trivial set of bit operations.
The problem is that it doesn't seem to scale: if I had 50 candidates and 256 voters, I'd need a tally of size 8*50=400 bits. It is my understanding that homomorphic schemes and big integers are not a very efficient combination. However, I cannot find a scenario that addresses this problem and shows that it is feasible in a country wide scenario (where voters can be hundreds of thousands, or even millions, and candidates can get up to a few hundreds), or, quite the opposite, clearly states the practical limits of homomorphic tallying.
Am I missing something? Is homomorphic tallying as restricted as it seems? If so, why is it regarded so highly as a building block for online voting?