I think anything in first has to address those issues. Either the letters/diary thing, which I call "first headlong" meaning that the narrator doesn't know in advance how things are going to come out, and you're carried along at the same pace, or else you have to have a time and place and purpose for which the whole thing is being written. In all my published first person novels I explicitly address the issue of memory -- cheating with giving Sulien the same kind of good memory I have, and with Lucy in Farthing explicitly saying about dialogue that mostly she's just saying what she sort of remembers they said, but this next bit is word-for-word, sort of thing. In Ha'Penny and Half a Crown I have a time and place and purpose but I just let the memory thing glide.

I don't like letters and diary, I don't mind reading them, but I don't like writing them because characters change and grow as time goes by, which I'm fine with, but I don't want to have to deal with as regards narrative voice. Though now I think of it, it might be fun. But it also would be quite a hard mode for me, I think, I'd have to be very aware of that. The times I have tried it, I had problems.

The other form of first is what I call "brain dump" where it isn't being written (or recorded, like Vlad), you're being carried along inside the head of the first person voice, often in present tense.