There is a theoretical justification. The sum of Poisson RVs (random variables) is Poisson. Raw counts of uniquely assigned reads to genes are very close to Poisson distribution across technical replicates. And the statistical model includes Poisson RVs or RVs with higher dispersion (due to biological variation). So the sum is a good idea for summarizing technical replicates.
Note that the average of Poissons is not Poisson, for example, it has less variance than the mean. Suppose we take the mean of 5 Poisson RVs with lambda=10 and call this new thing X. The expected value will be 10,
> mean(replicate(1000, mean(rpois(5, lambda=10))))
[1] 9.9804
but the variance of X is now less than the mean:
> var(replicate(1000, mean(rpois(5, lambda=10))))
[1] 1.951687
This kind of a RV, a count which is underdispersed, is not possible to model with the countbased methods.
