Or in a much simpler and common case: you trust someone right now to run a non-modified client and not to take screenshots, for example based on a corporate policy.
Months later the relationship turns sour, and they are fired or denied a promotion. They can't then go through the archives any more to take the screenshots.
Or even extract the text + signature before it "explodes". Keybase messages don't have repudiability so anybody who has received a sign message should be considered to always have that message.