I've decided to do some research online to understand complements better. Chinese Grammar Wiki said:

"You might be wondering: when do I use a complement? That's a good question, because often there are non-complement ways to express what the complement expresses. For example, do you use the 不了 complement after a verb, or do you put 不能 before the verb? Do you use an adverb before the verb (快快地跑), or do you put the same information in a complement after the verb (跑得快)?"

I got excited as I read this because this is exactly the question I had in mind and wanted the answer to. Then I read on..

"The sad answer is that it depends. There are many factors involved. As a learner, the best thing you can do is to memorize the complements you encounter the most often, and start using them."

Sigh... I find answers like this so frustrating. I really would like an explanation of those "many factors involved", but haven't been able to find them online so far.

Can anyone here help me with this question?