There are a lot of resolution standards; 480p, 576p, 720p, 768p, 1080p. Not all of them are mainstream and the only source you'll find for some of them is your PC. I don't agree w/ your argument about 1366x768 being made for 1080i. 1080i & 1080p look best on a native 1920x1080 resolution monitor. 720p looks best on a 720p monitor. My projector is 720p native and 1080i images look great on it. I don't think a 1366x768 monitor will make it look much if any better. 1080i/p is a fairly even multiple of 720p (2.25), so scaling should be a lot simpler than from 720p to 768p (0.878477306...), or from 1080i /p to 768p (1.97657394...).
I believe that 1366x768 monitors have a different reason for existence since there isn't any 768p source material out there. A very standard 4:3 PC resolution is 1024x768. If a 1366x768 monitor receives a 1024x768 signal it can display it w/ 1:1 pixel mapping w/ black bars on the sides. It is important to have 1:1 pixel mapping with PC signals as it makes text a lot easier to read.