Multimode transceivers are still a slight bit cheaper ($30 for 10GBASE-LR vs $22 for 10GBASE-SR on fs.com) but that's more than offset by the single mode fiber being slightly cheaper, even for short distances.

Apples to oranges. SR is for short runs inside a building. LR is for sending signals across a city.

For short runs inside a building, the transceiver prices are much more comparable. Compare https://www.fs.com/products/251819.html?now_cid=4089 to https://www.fs.com/products/282973.html?now_cid=4089

SR is for when you accidentally installed MMF really.

Except, no, you can run (single lambda, not muxed) LR transceivers on MMF, it's out if spec but you actually get around +20% range before hitting dispersion limits.

I'll also note SR ranges are not in fact long enough for larger buildings. And this gets worse with higher speeds, since modal dispersion is a bandwidth problem, not attenuation.

Also, using 800G for comparison is a bit ludicrous ;). 10G is bread&butter, 25G/100G is mainline. (40G is the shunned weirdo uncle.)

Historically, the price difference between MMF and SMF transceivers was greatest at the highest speeds. That doesn't seem to be the case anymore for short-range transceivers.

Why does multi mode sound like it should carry more bandwidth but from context seems to be the less interesting option?

Mode is simply the wavepattern of the light traveling through the optical fiber. Multimode means there are a few different wavepatterns traveling down the fiber, they tend to potentially interfere and its not as efficient of a use of optical power. In singlemode, this is a lot harder to do and requires better optics, the light is in one pattern, power is efficiently allocated to that pattern, and thus the light can be sent much further. Its been many years since college so hopefully that explanation suffices.

Now lets say you want to send multiple signals to get more bandwidth on one fiber, you just need to move the frequency/wavelength of light so different signals have different wavelengths and can be discerned at the receiving end. That's gonna take even more optics and filters on both ends, but works quite well to add more bandwidth to existing fiber installations where running more fiber would cost a lot more than installing new equipment on the ends.

Rather than interfering with each other multimode suffers mainly from modal dispersion as the modes do not travel the same path and some take a shorter or longer one, so the signal is spread out.

It's DAC in rack and then fiber or copper between spine and leaf (depends on distance, etc).