OK, just to clarify, your post has the question about whether the Phonak Audeo Lumity L90R’s work with “any” rechargeable charging case? Cuz if that’s what you’re asking, I believe the answer is that they need an “induction” style charging base that does indeed come with the aids when you purchase a pair.
You’re SPOT ON with the observation about their rechargeable batteries not even lasting ONE FULL DAY. I’d like to see how the Prez of Phonak travels if s/he wears rechargeables and is going overseas on a long flight with Customs on each end. Y’better have a backup pair of aids or that battery brick you refer to, cuz the last thing you want is DEAD batteries staring down a Customs officer.
When I travel I have my backup Lumity Life aids AND a pair of older battery operated Marvels. O’course that also means I have to bring along at least ONE induction charging base, power cord and a couple weeks’ worth of size 13 batteries. And then there’s the Roger ON iN V2. I pack that with its own charging base and power cord as well. Let’s see, did I forget anything? Cuz I may not have room for a toothbrush if this keeps up. 
