As mentioned, one of the advantages of suppositories is that the drug gets delivered directly to your blood stream. For molecules that degrade in stomach acid and need to be absorbed in a more neutral pH environment, going in via a suppository saves the company from having to design a drug that is coated to survive the stomach and then release the drug once in the intestine. It also provides much more rapid effects, which is a good thing for cold and anti-allergy medications, which people want fast-acting relief.
Fun fact: one of the tests on a suppository drug lot is “melting temperature”. The manufacturer needs to ensure that the wax binding will melt above room temp but below body temp - usually criteria are something like 34-36C, IIRC. It’s one of those time-consuming but zero effort quality control tests that are absolutely fantastic to do on a Friday afternoon, when you don’t want to work anyways. Just watch a plug of wax melt in a capillary tube.
