I'm writing a story in a diary format. I'm including both conversations written out like in a novel (direct speech, formatted with a new line for each speaker, etc) and also paragraphs that summarise a conversation. The former is for longer, more important conversations and the latter is for short conversations, or long ones that can be summarised in a sentence or two (e.g. "we talked about the rugby"). I find that too much indirect speech can get tiresome and it's hard to stop the paragraph from being a list of "and then I said" "and then she said" etc etc.
The potential issues with a diary with fully formatted conversations is that a) the person writing the diary may not remember the exact words and b) they might not bother to format the conversations properly - indirect speech tends to be more diary-like, however IMO it's not implausible that someone can remember the main parts of important conversations and know how to write them out properly.