Sure, coin collecting may seem like a solitary pursuit, but just remember: Cool cats collect coins. What is the purpose of the alliteration in this sentence?

The purpose of alliteration in this sentence is to make the 'slogan' stick in people's minds. This person is trying to make coin collecting sound like a fun activity that people will want to do, and using alliteration like this will have them easily remember the slogan long after they've read it.