Does that not make any sense? Great.
The name 'Podcast' was created for an audio file created by whoever had the means or desire to create an audio file and uploaded to the interweb so that people with the means or desire to listen to said audio file could do so on-demand by streaming the file. The majority means that people with the desire to listen to these audio files were the iPod, which was essentially an iPhone without the phone or messaging or apps, or, as it were, an iPhone but only with the music and the 'Podcasts,' which as pointed out, was named as such for the iPod.
'Podcasts' are more generically known as 'Netcasts,' at least as far as the author(s) of the Wikipedia page for 'Podcasts.' 'Netcasts' is nearly as silly and unfitting a name for 'Podcasts' as 'Podcasts' is. Personally, just to reiterate, I don't like either name.
Thus and so I propose the name 'Streaming Internet Audio Program.' It is certainly longer than 'Podcast' but it isn't nearly as dumb. It sounds less hokey and less amateur. Also, you can shorten 'Streaming Internet Audio Program' to 'I.A.P.,' or 'StrIAP.' 'StrIAP' is pretty stupid, though.
Secondly, I have an idea for a streaming internet audio program. I will share that idea when I've thought about it more and when I am sure that the word 'Podcast' is no longer being used. So, it's really up to the people.