As I see it, Troi was made half-human just to have weaker telepathic abilities than full Betazoids. She could only sense feelings, because if she could read minds it would be too easy to solve every problem in the series as soon as it was introduced. Not that she was used at her full potential in the series anyway, but whatever...
Also, using the same principle, wouldn't a Human-Vulcan hybrid like Spock be able to become way more logical than a full Vulcan, because, as a Human in comparison to the Vulcans, he would have weaker feelings to suppress, since Vulcans have way stronger feelings than Humans?
Yes but if they hadn't made Betazoids powerful telepaths in the first place, they would not have needed to make Troi half-human to put the genie back in the bottle.
Spock was a more powerful telepath than most Vulcans and I don't think tehy ever really made much of his human heritage - or at least nothing that wasn't also attributed to full-blooded Vulcans in later series.
I love Andorians actually. Best thing Enterprise did was to finally give them some air time. Both species have a lot of inherent traits. Mixing and matching them would be a bit of a nightmare.