Then you have to decide for yourself if you're OK with that or not.
I know Microsoft looks at my files when I put them on my OneDrive. I take that into account when I decide what to put there. I know Google reads my mail when Thunderbird sends it through their SMTP servers. I know it'll be read by some unknown parties along the way to the recipient. I take that into account when I write my mail.
If I pasted a URL into a feed reader, I'd most certainly assume the app, and by extension its creators, would access that URL and read what's there. I'd take that into account when using the app.
Then I wouldn't be surprised.
I haven't read Thunderbirds privacy policy in detail, so for all I know there's a clause about collecting email addresses in there. Could even be for a good reason, spam filtering for example.
And as mentioned I take that into account when writing emails. I do indeed avoid writing certain stuff and avoid sending certain mails due to privacy. For the rest I see it as an acceptable risk/reward tradeoff.
I'm not a tinfoil hat kinda guy, but the innocence is gone when it comes to modern software.
In, fact URLs by design explicitly supported passwords.
A password can be leaked just as well as any URL, particularly if the password needs to be periodically sent to a downstream server to do the feed polling, and hence stored in plaintext.
URLs generally have less protection than a password because that's how we design a lot of our systems (and this is a property of our systems and not of the URLs themselves), but the protection they do have is often enough.
You protect podcast feeds for revenue, not privacy. The negligible loss of revenue you're going to experience if somebody hacks into a feed reader isn't worth inventing a new protocol. You need to protect against abusive sharing of URLs by authorized users anyway, usually by having a system that forces the url to be re-generated when it's getting too many visits, so if one of these databases becomes fully public, the problem is already solved anyway.
Everyone needs to accept the fact there's no such thing as a private URL. There are URLs that can be originally communicated to you privately—through a private channel, that is—but insisting on holding onto some (wrong) belief that we can or should be able to mint URLs that themselves possess some "private" quality goes against the fundamental design of the Web and what a URL even is.
(Yes, this does mean that every podcaster that implements subscriptions by giving one feed URL to free listeners and having listeners who pay for premium content use a different URL is fundamentally broken. Yes, this does mean that that big engineering organization that implemented file uploads and read/write access through slugs consisting of unguessable 128+ bit tokens is also wrong.)