Which radicals are used mostly just as phonetic?
This is an interesting question.

Before I say anything I should warn you that I am not a linguist and some of my terminology could be off. Just to share some of my insight as a native Chinese speaker and hopefully you will find it helpful.

I think there's some information lost in translation. 

There're two related, similar but not interchangeable concepts called 偏旁(偏 means partial, 旁 means on the side) and 部首(literally means "section header"). However they are both translated as "radical".

While they are both components of Chinese characters, there are differences. From their literal meaning, you can loosely think 偏旁 as a partially-formed 部首 placing on one side of a character. With that in mind, 部首s are mostly used for classification purpose (as in a dictionary) and 偏旁 are mostly used when talking about character structure and composition (as in this question). But don't worry about that too much, since many native Chinese speakers couldn't tell the difference all the time either. 

Take 阜 and 阝for example, you can see right away that 阝is a simplified version of 阜, hence it's a partial (偏) form of 阜. You can put it on the left side of a character, as in 阴, 阳. As well as on the right side, as in 邓, 都, 部 (though in this case, 阝is short for 邑 instead). In both situations, they have no contributions to the characters pronunciation.

Some other examples:


水 and 氵
心 and 忄
金 and 钅


To sum it up, 偏旁s almost never convey phonetic information, while 部首s (in the context of character composition, not for classification) sometimes do. 偏旁s almost always have something directly to do with characters meaning, while 部首s only sometimes and indirectly do. So it's not an exact science.