Honestly, what's the point of hybrid characters? The only good reason to have one is to hold a mirror up to the human condition in some way.
Spock's Vulcan-human mixture highlighted the internal struggle that most, if not all, people face at some point in their lives. But you can't really do that kind of "torn between two halves" thing anymore because it forces you to ignorantly assume that all races EXCEPT humans have built-in, predetermined personality traits. It's not okay to assume that all Asians are computer nerds or all African-Americans are rappers, so why would it be okay to assume that all Klingons are warriors or all Ferengi are greedy? It's not believable
Ziyal's hybrid nature nicely illustrated the condition of people whose parents belong to two different national or ethnic groups that do not get along. Ziyal was never "torn between two halves". She was a whole person-Ziyal-who at times found herself torn between two cultures without fitting into either of them. This is a dilemma faced by many folks here in modern society, so it resonates. In my opinion, this is the only way you can pull off a hybrid character believably now.
But 99.9% of the time, especially in fanfic, the only point in having a "hybrid" character is just to be all fanwanky. Your helm officer is a Klingon-Bolian hybrid? What does that even mean? Either it doesn't figure into the plot at all, or the author does that "character torn between two halves" thing that the Original Series already did, only they do it way worse.
Also, a profusion of hybrid characters makes a story veer too close to comic book science, in my opinion. If two mammals from Earth-say, a horse and a moose-can't interbreed, why the heck would two people from completely different planets be able to interbreed easily? On the 1975 album "Inside Star Trek", there's an "interview" between Gene Roddenberry and Mark Lenard as Sarek where it's revealed that it took a whole lot of medical intervention for Spock to come into being. Such hybrid births, therefore, should be exceedingly rare and not possible in all cases.
Again, just my two cents.