Why play podcasts on a website?
Podcasts were originally designed to be downloaded, and that's still a fine idea. But modern podcast apps also support streaming on demand, which is great for trying out a new podcast before you subscribe to it.
Player FM further removes the friction by making a podcast app available inside a web browser — no install required. Furthermore, for people who do use the mobile apps, a desktop web browser can make it a lot easier to manage their subscriptions and find new shows.