Officially released music only available as limited time downloads or streams

An example would be "The Swell Season" in 2008 recorded most of their shows and made them available as downloads that you could purchase. Another would be when Wolfgang's Vault opened you could (with a membership) purchase/download hundreds of shows (although the question of ownership was not truly resolved).
Or all the shows that have been streaming for the last year due to covid - lots of my favorite artists have released a lot of live material (Rickie Lee Jones, Darden Smith, Indigo Girls, Howard Jones, etc). Some of the shows have ended up on youtube but many of these shows are now no longer available (through the original websites) and it makes me wonder in the future how will these type of shows be viewed as far as an artists catalog? I'm assuming much of it will never be re-released which is a shame because there's a lot of great stuff that's out there.

 

There are albums released via iTunes in a series called iTunes Originals that likely qualify for what you mean. For example I have Willie Nelson iTunes Original, which is an album of basically live in studio tracks with interview tracks interspersed in between.
Edit: Hard to quantify where it fits into the catalog as a whole, but with someone like Willie with countless compilations released as it is I’m not sure how much it matters. It is just more product, and in this case probably not product that will have any significant impact.

 

Secret Machines
“The Poison Tree”

It was an iTunes only bonus track that was included with their 2008 self titled album. The album is still available on iTunes but without the bonus track. It’s not even on YouTube!

 

The band Best Coast (basically a 2010s power pop band - I think they are good to very good) has at least one iTunes Originals release that has come up in my Pandora mix. What annoys me is I can't easily buy songs from that release; in the case I have in mind, I like the iTunes Originals version much better than the regular studio version!

Those iTunes Originals are at least somewhat like the BBC recordings (probably most famously recorded by John Peel for many years) that many bands have done.

 

A live performance of McCartney's "Ocean's Kingdom" was included with the download. Don't believe that's been available otherwise.

 

I think the only album I have that was streamed or avail for Download for a time was a Covers album Scott Weiland did I had to buy it from his website. Some of the tracks i had from his solo albums but there were some that were new to me, like him doing Farmer Frances Has her Revenge on Seattle (Nirvana) and i think another Bowie Cover which was Jean Genie I think id have to look to be sure

 

Another one I though of was the download of 4 live shows that came with Blue Oyster Cults "Complete Columbia Albums" collection. I took too long to actually open the box set - by the time I did the codes had expired.

 

When Black Crows ‘Lions’ came out it had a similar gimmick to pick a live show for download as part of a promo insert. There was one available from Stubbs in Austin that I was at. Have never seen that offered again.

 

King Crimson shows from dgmlive.com have eventually found there way into their mega-boxes.

 

Information Society's-2014 album _hello world had a 'data' track
Put it in a sound editor and it gave you a web address for some extra tracks/mixes. Pretty neat.
It's long gone now.

 

Wow. That's some out-of-the-box thinking, there. Wonder who made that happen, the artist, or the label promotion department.

 

Probably one of the guys
Being a bunch of geeks, really no surprise. You should check out their 1988 debut CD+G

 

Sorry, I guess I just don't have the pure energy anymore...

 

The Beatles Bootleg Recordings 1963 - Wikipedia

 

I'm pretty sure this 2010 split EP isn't available anywhere nowadays:
Centro-matic/South San Gabriel- Eyas

 

Same with “Sessions@AOL.”

 

Radiohead's 1996-1997 demos ripped from mindiscs, after showing up they were sold for 21 days from the band digital only - smart move and free publicity for stuff you haven't heard in 20 years

 

Somewhere between 15 and 20 songs that made the Top 40 of the Billboard Hot 100 in the 21st Century were download-only, never on physical format in their hit version, and no longer available as legal downloads.

Most of these were short-term charity releases. Others were by American Idol contestants or alumni. Some were both.

None of them had any staying power, probably because of their limited availability, but one of them made the top 10:

"I'll Stand By You" by Carrie Underwood (her cover of the Pretenders song) peaked at #6 on May 12, 2007. It was a studio recording released for the charity "Idol Gives Back." You can hear it on YouTube, but it's officially deleted.