Requested feature overview description.
The 'Show reduced samples option',

Large images will be replaced with a smaller version, which may reduce image quality, but loads faster. Good for mobile devices or slow/metered internet connections.

Doesn't seem to include animated images (gif, webm, flash etc), or anything other than the standard static image formats

Why would it be useful?
Easier on 'low end' hardware, mobile etc.

I wonder how many people can say their hardware can comfortably render files like these:

post #828019 - largest animated gif
Size: 1280x720 (74.9 MB)

post #981572 - highest resolution gif
Size: 1500x2940 (5.4 MB)

post #950016 - largest animated post
Size: 720x480 (100 MB)

What part(s) of the site page(s) are affected?

• Post display
• */post/show/*

• Content delivery (?)

• other (??)

By the way, reduced samples doesn't work on non-animated GIFs either.

WebMs I always test on my phone before uploading. Unless it's some super crazy resolution high framerate file, it usually works on mobile wonderfully. That 100 MB file works even on lower end mobile devices as it's only under 1mbps bitrate, browser does all the buffering while playing the file. It's 16 minutes long so filesize is larger naturally.
With those it's usually safe to say that if post has hi_res high_framerate tags, it won't play well on low end/mobile. Filesize tells nothing about it, it's combination of resolution, framerate and bitrate.

With flash files, those usually work just fine even if they are larger and you usually do not need to think about mobile compatibility as only ways to watch those on mobile is third party browsers™ with cloud technology® or using outdated versions of flash, without latest security patches and features. Also there's usually no way to modify them in any way to be less demanding by automation.

Bigger problem are the gif files and webm files with insane bitrates. In my opinion, when gif starts to go above 10 MB mark, it's too big. It was never meant to contain HD high frame rate material like in that first example gif, because of limited colorspace and highest useable frame rate being 50 FPS. With WebM it seems like there are converters/artists, who simply do not want to see any compression and might use something like 10 or even 25mbps bitrate, even though with most materials anything above 5mbps is overkill.

The main issue comes from sites guidelines: highest quality version is the one to stay. So even if someone posts animation in 10 MB gif, if someone converts the HD video version of it into 100 MB gif, that one stays. So yes, at this point site will need some sort of system to show much lower quality version of the gif files. Funnily enough, most sites simply convert gifs into HTML5 video formats, includes social medias, other gallery sites and messengers. Even with that first example, there is WebM version posted as parent post which weights 1.3 MB instead of 74.9 MB.

Both WebM and gifs files _should_ be really easy to automate be converted into all HTML5 video formats, which then should cover near 100% compatibility and allow specifying max limits like 30 FPS, 720p and 1mbps max, making them work with everything.