I understood that the purpose of these models was to give for each zero expression of a gene, the probability that the 0 is due to a technical bias or to the biological reality, right?
If I am right with this assumption, then will these models be used simply to choose in some algorithm which zeros will be taken into account and which will not? Do they have any other use?
The purpose of choosing a zero-inflated model over a non-inflated model is the same as the purpose of selecting a negative binomial model over a poisson model -- or a T distribution over a normal distribution -- it fits the data better, so inferences made from the models are more accurate and less biased. For instance, the paper that you linked shows that differential expression results could be biased if a zero-inflated model is not used.