If there is proof that certain aspects of English appeal to the aesthete, it is parallel structures. Parallel structures can make what you write and what you say memorable. If you closely observe most the quotable quotes, you will start noticing that most of them have parallel structure hidden in them. Take a look at this for instance:

So, how are these relevant to IELTS, GRE, or PTE coaching?

For language tests, they will help you get a better score in speaking and writing. And in tests like GRE and GMAT, they will help you understand the nuanced differences. It is sad that more coaching sessions do not focus on this beautiful part of language!

Here is the quiz on parallel structure: