Why should a distribution being pseudorandom strictly be a sequence of distributions being pseudorandom
A sequence of distributions is a definition of a distribution for each $n$. For example, consider the distribution $Dist_n$ to be a string of length $l(n)$ generated using some pseudorandom generator with a seed of length $n$. Then, for each $n$, the distribution is actually different. The reason why technically you need this is because the notion of negligible is asymptotic - it needs to be a function so that for every polynomial, the function is smaller than it for some large enough $n$.