EDIT: I want to add that "training on chat logs" isn't even the issue. In fact it understates the danger. It's better to imagine things like this: when a future ad-bot or influence-bot talks to you, it will receive your past chatlogs with other bots as context, useful to know what'll work on you or not.
EDIT 2: And your chatlogs with other people I guess, if they happened on a platform that stored them and later got desperate enough to sell them. This is just getting worse and worse as I think about it.