I want to add a quick disclaimer that my premise could easily be wrong. It comes from 3 simple things: there’s a Wikipedia page on Dionysus-Osiris syncretism but not Hades-Osiris, the Herodotus quote, and Dionysus-Osiris syncretism being mentioned in passing in this excellent askhistorians answer. Not enough evidence to pass academic muster (doesn’t prove Dionysus-Osiris syncretism was more common) but that’s the privilege of being the question-asker.
Also I understand that these gods shifted and molded into one another frequently with many “domains.” And that not all gods were seen the same way depending on the region. Correct me if I’m wrong but I believe that both Dionysus and Osiris were gods of fertility. Still, if Osiris was the judge of the dead in later Egyptian eras, it seems to me his main “role” (if there is a main one) overlaps most with Hades, ruler of the underworld.
Syncretism is a little bit of a sneaky word. It isn't actually meant to explain anything. It's a word for describing a result.
The processes at work in linking up god names are complex, obscure, and historically and theologically contingent. There's no system, in other words. No one sat down and said 'OK, Hades and Osiris are both in the underworld, so we'll equate them with one another.' It's all the result of ad hoc and inscrutable processes. 'Syncretism' just bundles all the processes up and looks at the end-product -- namely an equation between Osiris and Dionysus, or Osiris and Adonis, or Isis and Selene, or Isis and Demeter, and so on.
In some cases of interpretatio graeca/romana there was more of a systematic approach, but that isn't the case in Herodotus' treatment of Egyptian gods. The communities he was in contact with were already ethnically mixed: for example at the Siwa Oasis, where he writes (2.42) that the people there -- the 'Ammonians' -- were 'colonists from Egypt and Ethiopia, and they customarily use speech that is in between both'. Egyptian and Greek religion were also interacting more and more with one another in his time, so the translations of names depended more on local practices than on a top-down systematic approach to the two pantheons.
In the case of Dionysus and Osiris, Herodotus describes a festival of Osiris in 2.47-49 that was evidently easiest for him to interpret in terms of Dionysiac festivals. The cult of Osiris involved pig sacrifice, which was normal in Greece but highly unusual in Egypt; and then 'they celebrate the rest of the festival for Dionysus roughly as the Greeks do, except for the dances', and phalluses are involved in both festivals but in different ways.
He goes on to write in 2.50 that most Greek divine names were in use in Egypt. He thinks they came originally from Egypt, and he's wrong in that, but it does indicate that Greek names were in circulation even among Egyptians. So there's a lot of concealed processes involved in syncretism even before Herodotus arrives on the scene.
The Adonis cult arrived in Egypt and Syria by the Hellenistic period, and once it did that seems to have become the preferred syncretism for Osiris. That may be because they're both dying gods. But again, the processes involved in syncretism aren't transparent and they're usually not systematic.