A really interesting intellectual property case (which is a great example of rich people exploiting the system for their own ends) is the recently resolved copyright lawsuit involving the "happy birthday" song. Maybe something for you to do in a future post. Worth looking up because its kind of hilarious.

Edit: https://www.theguardian.com/business/2016/feb/09/happy-birthday-song-lawsuit-warner-chappell-settlement happy birthday case

As to trademark, its more a matter of protecting your identity when you create a brand. Dr. Dre did not invent the term "beats" but it came to be associated with him. Because of this, if fucko-mcducko comes along and starts marketing shoddy headphones and calling then beats , its going to effect Dre's reputation.

Normally, a trademark only gives you exclusive rights over a competitor. So, for example, unless "this sick beat" is associated with a specific product, its not enforceable at all. And even if it is associated with a specific product, it can only be enforced if similar products are marked with that. If swift is trying to get one, it probably is going to end up on some clothing or electronics line that shes endorsing.