I keep all my BP stubs together... I hate getting the big part as yeah it's an extra that doesn't fit lol.
I know when they all go thermal the whole thing is moot.. but looking at the stub collection also reminds me of many previous memories.... like flying SQ in F to LHR, ot just yesterday the A380 to SYD.. or the first flight I was upgraded, or BA to SVO or the first 777 flight in 1995 or ... heaps of other memories