I think people started widely clamoring for more primates after the continent packs. Once a lot of zoo staples and old favorites were knocked out, people started looking to see what else was missing. Gibbons held the top spot followed by baboons, howler monkeys, and tamarins. Spider monkeys have surged in popularity more recently. Squirrel monkeys, golden snub-nosed monkeys, guerezas, and grey langurs/lion-tailed macaques were some popular choices among monkeys (which were generally kind of low), too. There was also support for geladas, sifakas, and aye-ayes, but I don't think they've ever been widely regarded as necessary, just popular.
Similar to the ducks, I think part of the reason for their initial low popularity is that they didn't seem possible or likely. The base game didn't have many, and we don't have a precedent for zoo management sims with a good primate roster. Also, if I'm being honest, I know a lot of people find monkeys a bit creepy and birds a bit boring. However, with Planet Zoo, I can build interesting climbing frames. Primates are very useful and fun for that, and they are needed for creating realistic zoos. A few more birds are also necessary for realistic zoos.
Most of the conversations about baboons were comparing them to geladas and other competition in various pack ideas. Now that the focus has turned more strongly on monkeys, habitat birds, and the degree to which both are missing, people care about baboons and other species a lot more.