Pairwise independence is to give the algorithm stronger guarantees and let it work with a simple hash function like ax+b, otherwise probably most existing algorithms can be simplified in the same way. The most similar algorithm is BJKST, which is almost identical except for specifyimg the sampling mechanism to require less randomness.
To someone who worked on this type of thing before, it's like seeing people familar with LLMs say "oh yet another X-billion parameter model on github doing more or less the same".