The reason why there is no series for demotion is that players would often just stop playing ranked if they're in it. Why risk getting demoted if you can just avoid ranked all together and stay in your rank forever. If you're plat+ and it's still a few months from the end of season, you'll have to play them eventually, but someone in gold V can just hold on till the next season.
That's probably the reasoning to hide the information about when you'll drop. However... Is the current system any better? If you're a 0 LP, you might also be afraid to play because you don't even know whether or not you'll drop if you lose. Maybe if it were a best of 3 series, you'd atleast have attempted one game.
I'm not so sure what's the best approach. I bet Riot has been digging deep into these matters too.