Same here. I didn't even think about it but Saix would be one of the last people I would expect to tell Roxas to use a diary.
As for the reason I imagine it was to help Roxas get his thoughts out and in order and help him acclimate to his new life as a Nobody and Organization member.
The real reason is every game has a journal and since Jiminy isn't in this Roxas got a diary. Though it seems they gave up on having a reason in BBS.
Saix handles the day-to-day work of the Organisation and who gives out most of the orders, so it's only logical that the "order" to keep a diary would come from him.
It's also him who orders the members to write and deliver their mission reports, so it could entirely be that Saix just had Roxas keep a diary in order for him to learn how to write so he can later on bring in proper mission reports.
Maybe he wanted roxas to develop a heart? Was there maybe some Isa left in him before DDD? Or maybe he believed roxas developing his own heart would be easier to turn into a vessel than ven's heart? Could ven's heart even be a viable option with it's pure light and all? Shit is confusing.
Err, I do not think that Saix was even aware of the possibility of a heart developing, as far as we know only Xemnas, Xigbar, Xehanort himself and DiZ knew about that such a thing was even possible.
Furthermore, he
certainly did not know about Ven's heart being in Roxas, Saix isn't even versed in how hearts work in general.
I actually doubt that
anyone except maybe Xehanort definitely knew that Ven's damaged heart was located inside Roxas. Mickey suspected something about the whereabouts of Ven's heart after Coded (as shown in the Secret ending) and several people, like i.e. Xigbar and Xemnas, might have suspected a connection between Roxas and Ventus due to the obvious physical similarities, but there's no indication that they specifically knew about Ven's damaged heart being directly there inside Roxas.
Last but not least though, Xehanort wants his intended vessels
without hearts. After the royal pain that he had with Terra, an opposing heart inside one of his intended vessels, he decided that empty vessels would be easier to use, which is why he even started the whole schmuck with the Nobodies and the experiments on hearts (as Xemnas explains in DDD).
Roxas developing an own heart (and thus his own identity and self-awareness) was what actually eventually made him
unsuitable as a vessel for Xehanort because he would have needed to subdue Roxas' own self in order to use the vessel like he had to do with Terra.
That's also why he put so much effort into drowning Sora's heart in Darkness during the course of DDD, because he wanted the actual
owner of the vessel, the original heart of it, out of the way so he wouldn't have another Terra-scenario.