I've heard him make the same statement and had the same thought. Is there any downside for them to add a BitTorrent option? Maybe it's just that they can't track the number of downloads?

If that's all, it seems like a small price for drastically reduced hosting costs. And if there isn't already, there should be a protocol for "distribute via BitTorrent but ping the original seeder to let them know".

There are two problems with it:

First you have to create the possibility for the people to download your podcast as a torrent. This sounds easy but is additional work. A new project that wants to tackle this is http://bitlove.org/ where podcasters just have to add their regular feed and the site will create a bittorrent feed and seed the torrents (extensive German descrpition: http://metaebene.me/2012/05/06/bitlove/)

The other problem is that users need to be able to easily download the torrent feeds. Some bittorrent clients support feeds, but right now only one podcast client understands bittorrent: http://http://www.getmiro.com/

If Apple were to take a leadership role here, that would help. If iTunes on desktop and mobile supported torrent downloads, the iTunes podcast directory would seed or link to seeds, and if there was some sort of protocol for pinging a centralized place to let content providers know how many times something was downloaded.

People have been putting torrent links in their RSS for years.

Yes, but it isn't particularly widespread, I checked the RSS for a few of my favorite podcasts and they don't have them. I also checked to see if any of my favorite podcast players support torrent downloads and they don't appear to.

I asked some folks at NPR about this a few years back.

I can't seem to find the exact message they sent me, but I believe the issue is that their licensing of content (mostly the music) on the show has specific rules about how that content is distributed (or not distributed).

Miro promotes and supports torrent based (video) podcasts. http://getmiro.com

Couldn't he put the file in Dropbox or Google docs get free downloads?

Both sites have a Terms of Service that prevent the misuse of their resources. If you've ever clicked on a popular link to a file on Dropbox's servers, you may find a page that tells you "This file has reached its daily limit of downloads" or something along those means. Google likely has something similar with Google Drive.