Interesting - totally different results from what I experienced, but great that it's worked out for you. I was syncing with a cable, if that makes a difference.
But my problem is now solved! After all those crashes my phone was so messed that I did the "Restore iPhone", and that got rid of the stupid wasted memory!
Note: about a month ago I did the Restore from Backup from iTunes, and that did NOT solve the problem - it didn't change the memory consumption at all. I was avoiding the full restore because (1) last time I did that, around six months ago, it took weeks for me to get everything set back up (different apps kept needing passwords that were only recorded on my computer at home), and (2) the problem with Podcasts Documents & Data came back anyway within a couple of weeks. However, this time I did Restore iPhone, and then it gives you the option to full reset or restore from backup - I chose the latter, so getting my phone back to normal was a lot more straightforward than I feared, and to my surprise it made the Documents & Data go away. I don't really understand why restoring the iPhone, and then choosing to restore from the backup, behaves differently than just restoring from backup (shouldn't it be the same thing?!), but so be it.
And now that I don't use the Podcasts app at all, I hope the Documents & Data won't balloon again.
TLDR: if you're no longer using the Podcasts app, Restore iPhone, and then choose to restore from a backup. That got rid of the extra Documents & Data for Podcasts for me. But if you're still using the Podcasts app, be warned that the memory may go up again.