I am a biologist and use different packages like DESeq, ... to normalize my data and find deferential expressed genes.  

Recently I have started to learn probability and statistics and I have studied distributions quite well. But I still have a problem: I think I do not very well understand why we really use this distributions to infer
expression levels for genes, normalization, find differential expressed genes? 

Why do we need e.g. Poisson model, negative binomial, ... for obtaining an approximate expression level? 
or in a package called mmseq: "Expression levels **are inferred** for each transcript using the mmseq program by modelling mappings of reads or read pairs (fragments) to sets of transcripts"!! why modeling?
why do we need to estimate expression level while we can directly count the number of reads per gene?

Or why is it appropriate to model read counts as a e.g. Poisson
process?

...

Is it only due to the fact that knowing the distribution (e.g negative binomial which can very well explain the observed counts, considering noise, ...) help us to apply the right properties like mean, var, ..., on data or there are more things to learn from the distributions?

Sorry if my question is primitive but it is a long time that I am struggling with that