We should be able to delete podcasts from our history. I only tried a few to see if I liked listening to podcasts but I don't. The few I listened to keeps showing up on my main page and I don't want to see them. There should be an option to close podcasts altogether or delete them from our history.
It looks like your idea was posted a while ago but, unfortunately, it hasn't gathered the minimum amount of votes to stay active in the Ideas Exchange (50 votes in the first 3 months). I'll mark your idea as "Closed - Not Enough Votes". You can learn more on how the Ideas Exchange works here.