There's plenty of time (and a World War) between Aleck's death and Westminster Archives acquiring the diary for any others to be lost or destroyed.
True, although on the positive side I'm fairly sure from what I've read that Aleck accumulated a collection of fairly valuable books going back hundreds of years. It seems inconceivable to me that someone would say "oh this is all junk" and bin it without first consulting a bookdealer. So at that point his collection would logically have gone to someone who appreciated its value. And the longer after that the diaries survived for, the less likely it would be that someone new acquiring them would see them as worthless. WWII is a possible problem, I agree, but then again the 1846 one survived. So any others that were stored with it during the war presumably did too.
Perhaps with all the current interest in Nat, the others, if they survive, might surface?
This is both a plus and a minus. I agree that if they are in private hands then the publicity about the Westminster serialisation could cause them to now come forward. The downside is that they would probably think that they have something that's extremely valuable in financial terms, in a way that they might not have considered before. Still that's a problem for Westminster Archive to ponder more than us

Historical footnote: My husband's 4x great aunt Mary Smith played hostess to Dr Johnson and Mr and Mrs Thrale on at least one occasion as she was married to Mr Thrale's cousin Ralph Smith of St Albans. I bet she was terrified of the real thing.
It's funny; in my ignorance I'd always assumed that his personality in that episode of the show was just some dramatic device to make the accidental destruction of the dictionary seem even more unfortunate. But I just did some reading on Johnson and it seems he really was notorious for his behaviour. Interesting that some people now think he had Tourette's (a term that didn't even exist while he was alive.)