It is a fair question, and for some teams it is the right answer — the files are structured, and shipping them as logs is not hard. Two things usually stop it. Cost: AI transcripts are large and log ingest is priced accordingly, so a year of retention on a hundred developers gets expensive fast for data that is read a handful of times. And shape: the useful artefact is not a log line, it is prompt, response and the resulting file diff joined together and browsable as a timeline. Log search will find the string; it will not show you what changed.
If you do decide to build it in-house on top of what you already run, the honest advice is to start by reading the on-disk formats rather than by asking developers to change how they work. That is the part we spent the most time on, and it is where a home-grown version usually stalls: eight tools, five formats, and each one changes between releases.