There is a T/B for 1080 but it is 1080p/24Hz and there is not much broadcast in that, so you are correct, that the current majortiy of T/B is 720p which then needs to be scaled to 1080 - I do not know of any passive TV that is 720p but there could be.
I also believe you are correct that SbS that is 1080i (the most common broadcast format) converts to all of the display formats easier than T/B. It is better for the Active TVs as there is better vertical resolution to work with.
Of course any 720p format will need to be scaled for any 1080p TV.
However the Frame Packed formats, that contain the highest resolution for each eye is the best for all TVs. The more information to work with the better the conversions will be.
There are a lot of formats but only 5 of them are mandatory. You can only be assured of a TV supporting the mandatory. The other formats are optional and different TVs may not support any of the optionals or only a few.