Q: Why no playlists in Podcasts?

On playlists: they are there, but they're called "stations". Go into the "My Podcasts" tab, press "+", and create a station. These stations are basically smart playlists - you can choose which podcasts will go in there, how to sort them, and so on. I believe the current stations are more powerful than in previous versions of the Podcasts app, although they're still nowhere near as good as the old days when I synced podcasts into the Music app through playlists on my desktop computer. (Mind you, those old days did rely upon syncing, and iPhones these days are more independent - thank goodness, because syncing no longer works!)

The "dumb playlist" functions are sorely lacking - you can fiddle with the "Up Next" list, but it's fiddly indeed.

I moved to Overcast a week ago and am enjoying it far more than the current iteration of Apple's Podcasts app - current-Overcast is probably about on a par with the previous version of Podcasts, which was perfectly acceptable. Overcast's playlist function is I believe currently a bit less powerful (but definitely easier to figure out!) than what the Podcasts app offers, and the Overcast app actually works. I can't say the same for the Podcasts app.

Caveat: my demands for playlists aren't that high. I usually just want a big list of all my podcast episodes, oldest to newest. Both Overcast and Podcasts can do that.

I agree that the "Featured" and "Top Charts" tabs are bizarre wastes of space. At least put the "Up Next" list there.

When you first create the station, there's an option at the top to "Include All Podcasts" - turn that on, and it should put all your podcasts in there.

Once you've already got a station, go into the Station Settings, and select you should see "Choose Podcasts" at the bottom - if you choose that option, you can select all of them, or specific ones.

Note that the station function only lets you do "smart" functions: for example, you can set it to include the two most recent unplayed episodes of Podcasts X, Y, and Z. But you can't choose "oh, that one episode of Podcast X that I haven't listened to, and those two episodes of Podcast Y." The Up Next function can theoretically do that (access that by pressing the three-dot icon that occasionally shows up), but I've found it awful to use.

I don't know why they're called stations - in my opinion it's one of the many missteps made by Apple in handling the Podcasts app.

Agree, this newest version is very cumbersome and the number one feature I use is missing:  a manual "on-the-go" playlist.

This app reflects very poorly on Apple and I will not recommend Apple products in the future if this continues.

No.  I appreciate that you're offering help on the closest available replacement for playlists, and if Stations works for you I'm happy for you, but it is not playlists under another name. 

Here's what playlists were, and should be:  When I go to a podcast episode, whether in Unplayed or My Podcasts, I should be able to easily add that single episode to a list.  Then I should be able to go to that list, edit the order, and play it.  Simple, clean, fast. 

Ever since Apple made the ridiculous assumption that I want to listen to all episodes of a podcast in a row, (Seriously, who wants that?  They're not songs in an album.  Play one and then stop; at the very least this should be an option, if not the default) I have been using playlists every day, and I have no desire to learn a confusing new system of inclusions, sort orders, and groupings, only to repeatedly spend time weeding out dozens of episodes I'm not ready to listen to yet... it feels like they're trying to force us to listen in the way they think we listen, instead of any way we want, and that they haven't taken many possible listening styles into account. 

If Apple's goal is to make us explore all the other podcast apps available until we end up buying one that does what we want, they are succeeding, but that's really not what I wanted to do with my time.  Just bring back On-The-Go, please.  It's been a staple of Apple mobile listening for so long; was somebody complaining about the availability of this function?

Well, it depends on your definitions. Stations are basically smart playlists with pretty limited options. They're (smart) playlists as I've always used them. I use playlists all the time, but I've never used them in the way you describe here, which is of course fine; the beauty of the way things used to be is that we could take different approaches. Now the options are more limited. As I said above, the "dumb"/manually managed playlists (i.e. on-the-go) options are awful. That doesn't particularly bother me because I've never used manually managed playlists very much, but rather just smart/automatic ones. The smart playlist options are moderately powerful on the current iteration, but man, the implementation and usability are garbage.

The Podcasts app got rid of the name playlists a long time ago - I'm not sure if it's ever had "playlists." They've definitely been called "stations" for a year or two. (I think the renaming is dumb and I don't know why Apple did it.)

Practical point #1: you don't have to listen to all of the episodes for a podcast in a row. There's an option in Station Settings, called "Group by Podcasts" or something like that - if you turn that off, then the episodes will be sorted separately, from oldest to newest, or newest to oldest, or your own manual order.

Practical point #2: you can play one episode and then stop. That's an option too. There's the sleep timer - the crescent moon at the bottom - and you can choose for the playback to stop at the end of the current episode. Mind you, other users have reported that it's unreliable.

Practical point #3: if you go to an episode, you can press that little three-dot icon and then add the episode to Up Next. You can then go that list, and play it. I'm not sure if you can edit the order - I think I once found a way to do it, but it's not something I really cared about too much so I didn't explore it. It's certainly not simple or fast trying to fumble for those little three-dot icons, but the option is there. Apple should get rid of those Charts or Popular buttons or whatever they are and replace one of them with the On-the-Go/Up Next function.

I've moved to Overcast because the current Podcast app has been hopelessly unstable and buggy, but for your playlist wishes, I don't think Overcast will be any better for you. As far as I've found they just have [smart] playlist/station options (whatever you want to call them), with nothing really equivalent to on-the-go. I'd welcome any corrections on that - as I said, I've never really used on-the-go and don't particularly want to, so I haven't dug too hard into finding that option.

True, playlists were already renamed but the on-the-go "station" still functioned like a playlist.

1 and 2: I don't mean one episode at a time within a station, I mean at any time. I should be able to go into a show under My Podcasts and play the oldest episode and have it just stop, no sleep timer required. That's an old change, but it's a huge reason why I started using on-the-go in the first place, and one of the main things that's missing when you compare on-the-go to Up Next.

3: Up Next certainly doesn't do what I want, but it's also not very good at doing what it does. Upon first entering the app, if I add something to Up Next, it doesn't start playing; it only works when something's already playing, and you can seemingly only access it from within a playing episode. It's painfully inconvenient.

I've been liking Overcast more, because you can set it to only play one at a time, but no, it doesn't do what I want either, and playback is often choppy. From the screenshot of iCatcher, it looks like it might suit my needs, but I am loath to spend even a mere $2.99 on something that was free just a few days ago, especially without getting to test it first. I'm holding out hope that Apple will fix this soon, but that doesn't seem to be their M.O.