There's a good chance that if you don't come up with the reasons yourself to use binary research it's not going to benefit you much anyway.
In the PBEM games I play, every turn I'm thinking about where the slider should be.
As a quick example, suppose setting the slider to 100% science means you would get the next tech in 4 turns, but you don't have enough gold to support that rate for 4 turns and at break-even you would get the tech in only 6 turns. Further suppose you have a library about to complete in 2 turns in a city with high commerce and/or beakers. In this case, it would probably be a good idea to set research to 0 for 2 turns until the library completes, then set it to 100% again after.
Even that example is hard to explain, and other factors would complicate things even further. The point is, binary research is basically extreme micromanagement that is not even going to do much for the players who know how to use it.
It's quite understandable IMO that people like DMOC who are used to using it, do it almost more out of laziness now than anything else.
Another reason to use it is that in MP you could mask how close you are to getting the next tech. It doesn't take much espionage for a rival to see your research, so if the info that player is getting is that you will have Civil Service in 600 turns
lol
, all he can work out is that you are at least intending to get that tech but not necessarily know how soon you can get it. Next turn he might discover you'll have it in 3 turns!
Even more cunning is that you could invest that free 1 beaker per turn into a completely irrelevant tech so that your rival can't know what tech you are intending to research. Once you have enough gold to be able to research the tech you want at 100% science the whole way, you switch only at that time and so give your opponent as little time as possible to know what tech you are researching.