I understand why Lilith wants Jade to expire. My suggestion is to let it expire slowly rather than in bulk at the end of a period. For example, if it expired at a rate of 10/day it would actually give an incentive to use it sooner, but should a player decide to hold onto it for a specific hero they could, provided that they have enough.
I will use myself as an example. I have Orkon, Goram, and Sylphi. I do not plan on buying anymore of their SS from CS. I also have 260 Jade from Orkon. At this point the only way I would use the CS is for Desmond or the next hero, which is 3 weeks away. If Desmond appears tomorrow on the last day of this Jade cycle, then I will do up to 10 pulls for Desmond then hard summon him with Jade if I don't get him before. If any other hero is there, I will save my 4000 diamonds and let my Jade go to waste. I do not plan on buying the next CS hero because I have so many heroes I need to gear already, and with the CS drop rates I feel like my diamonds would help me better with gear at this point than another character who will need more gear. I am assuming 360 pulls for any hero at this point before I even try CS without Jade.
Now, with my suggestion, I would have 190 Jade instead of 260 as of today since some would have expired since I pulled Orkon a week ago. If Desmond appears in CS tomorrow, I would have to do 8 more pulls (-10 Jade tomorrow) before being able to Jade pull him. If he shows up another week later, I would need 24 pulls to guarantee a Jade pull. I believe that the increasing prices might create a sense of urgency to use the Jade, more people will do more frequent CS pulls because the value of their Jade stockpile decreases, and players would have more flexibility on when to use it without a hard reset to 0. For what I assume is a concern to the devs about people buying the next new hero with Jade, keep in mind there would be 22-28 days between the summoning of the last new CS hero and the next one; 360 Jade 22 days later means they would have had to spend 23,200 on the previous CS hero. That's still a lot of revenue from CS.