I trust the in-game report system to cover the vast majority of cases (99.9% or so), it's accurate and efficient enough to do so, and has sufficient manual oversight to keep it on track. It hits the nail on the head almost every time, and it may get it wrong on those rare instances, but that will happen with any system (even happens with manual reviews from time to time).
Reporting via Support is a great way to address those cases where you think the standard systems wont manage, such as the much more "nuanced" breaches of the rules that the automated systems just don't know how to deal with. It's not something you would use for any old case, that will just take up unnecessary resources that Support has to deal with things that don't really need a manual input. It's really more of a "back-up" for those edge cases, or in situations where you can't use the in-game report system.