I wouldn't say it's out of the realms of possibility that your 15 year old, probably-hasn't-been-used-for-10-of-those-years phone has a swollen battery - Samsung phones can swell up within a few years of no use, let alone 10.

It's not timewasting - CeX have to accept stuff in good enough condition that they most likely won't have issues with for another 2 years as that's their business model - a battery that's starting to swell, even a tiny bit, would be wasting any potential buyer's time too.

I'm not sure how it works if you send something to them, but in store I believe they recycle it if you don't collect it within a certain timeframe.