Would it be possible for GOG to provide access to older offline installers for games? I've had a few that have been totally broken on older operating systems with no warning despite paying for something that previously worked on them.

Short answer, yes.
The solution gog gives is that install galaxy and use the rollback function in some games to restore a previous version. Then you can make a backup of the game folder.

If it's the offline installers, you're asking for: just wait for GOG's soon to be introduced subscription service.

Technically possible, most definitely.
Will they do it? No, because they want everyone on Galaxy, which does provide the rollback function.
Well, like BreOl72 pointed out, either that or paying for a monthly subscription when they'll launch the service they tried to test the waters for with that survey, access to older versions being among the suggested perks...

If you really want to know more about it, there are some threads about the problem and community discussed a lot about it too (in both threads there are links to other threads and game specific forum threads and posts about the problems):

https://www.gog.com/forum/general/preservation_program_killing_offline_installers_preservation
https://www.gog.com/forum/general/stop_this_madness_preservation_program_is_killing_games

And my guide if you wish to download galaxy builds on/through Linux using lgogdownloader:
https://www.gog.com/forum/general/guide_how_to_download_pre_preservation_program_game_versions_on_linux

It's simple: Always download the offline installers of all your games to your hard drive and keep them as a local backup which is out of Gog's reach.

One does wonder if that suggested perk would be for those who download the Offline Installers or just an extension to Galaxy's rollback feature.

As I don't use Galaxy, I don't know how extensive the rollback feature is or what might govern it.

For instance, if I buy a game today, do I instantly get access to older versions?
Or is the furthest I can go back, the version I paid for?

And how far back does Galaxy go?
If for instance, I bought a game from GOG in 2017, and it worked great on Windows 7, but the later versions don't, can I go back far enough to get that older 2017 version?

On a personal note, I've always downloaded my games immediately after purchasing them, and keep backups, so I can at least always go back that far with the Offline Installers. But no doubt a lot of customers at GOG haven't been that diligent.

And not always economical for all users... and sometimes sh*t happens and we lose or overwrite the immediately previous version.

Galaxy allows the user access to five versions. The current one, and the four preceding it. So how far back in time you are able to go depends entirely on the game. Something updated infrequently may stretch back ten years, and something like Astrea: Six-Sided Oracles which has thirteen versions in three years only goes back eight months. The old games that aren't being actively developed when they are introduced to GOG are the most safe in this regard.

It proves the staff are so out of touch with reality, they seem to think making gog like steam is a good idea. If they turn gog into another steam, but with worse service, everyone packs up and moves to steam or quits gaming....or the shady alternative

¯\_(ツ)_/¯

It is ironic, staff can already provide offline installers several versions back. They just choose not to.

Yeah I haven't, I have sporadically backed things up but never at the point of purchase. I downloaded my library recently in it's entirety with lgogdownloader and using those installers is where I started to run into issues. I know I'm in the vast minority of customers trying to run this stuff on older OSes, but it did work when I paid for it and I never got the impression that compatibility would change arbitrarily.

Oh, it does, for a long time now.

That used to be the case, but for several months now, many old games continually get updates, seemingly due to GOG's preservation program or adverts or something.

Thanks for the other information.

...which doesn't work for people like me who don't access the internet on their gaming computer and therefore cannot use Galaxy even if we wanted to (which I don't). I'm pretty sure the library would have a problem with me trying to install Galaxy on their computers. ;) This issue may be my single-biggest complaint against GOG, is that as a non-Galaxy user I cannot access older versions of the installers.