Most arts I can think of do a combination of simple but effective things, and more complex looking things (which can also be effective). I'll give you an example. In the beginning, after having reached a minimal required level of physical conditioning through calisthenics and form practice, our typical training day would include 1.5 hours of basic technique practice. We would normally focus on 2 out of 6 types of blocks/parries and appropriate counterattacks with those blocks/parries. Very tedious work that builds skill quickly. Afterwards, we'd spend about .5 hours to an hour doing applications, which were the fancy stuff you're mentioning. We call them "applications" because that's what they are, techniques designed to open your eyes to the versatility of the things you just drilled in combat situations. The training was similar shotokan and aiki-jujutsu in terms of how the training was structured. I imagine it's the same for thai boxing if Tony Jaa movies are to be believed.

What I've found, is the fancy stuff ends up being successfully used faaar more often against untrained/poorly trained combatants, while against well trained combatants, you're relying heavily on the basic stuff. What I mean by that is, you might find opportunity in an exchange to apply a "fancy" technique, but the better your opponent is, the more likely he is to sense the impending danger and respond appropriately, forcing you to abandon the technique and adjust as appropriate. This usually means falling back to a basic parry/counterattack. Even against skilled opponents though, you can still often land those fancy techniques and they can be fight enders.