From what I can gather from lists of "pros and cons" like this one, systematic sampling is roughly equivalent to simple random sampling when the list is randomly sorted. If not, it leads to sampling bias.
With this information, my conclusion would be that systematic sampling had a use before (pseudo)random numbers could be easily generated, but I can think of no practical use nowadays.
Are there situations where systematic sampling is still used? I am curious because it is usually included in all lists of sampling methods, but I'm unsure if it's just some sort of "historical inertia".