It's a good question! Humans as apes are more genetically similar to other apes than tailed monkeys, and that small difference (e.g. 1-2% of dna) has a huge impact on development. When animal research is carried out there is lots of preparation with model cell lines, organoids, tissue cultures, etc., before you get to the actual animal in the cage. With all that effort put into preparation, you want the final animal samples to be as close to human samples as possible.

Other simians also have different diets, microbiomes and are susceptible/resistant to different diseases than humans, which could definitely affect your immunology experiments.

However, the scientific benefits of using our closest relatives (i.e. humans, chimps and bonobos) is outweighed by the ethics of using highly intelligent and emotional organisms for research when alternatives are available. Ultimately, this is a socially constructed limitation but it's one I agree with. Also, it is very very expensive to raise great apes in captivity, which means research budgets can't cover it. Imagine raising a 60kg human with emotional problems that can bench 150kg for years just to cut it open and look at its colon. That's not worth it.