They want to get there (embedded ads that look like content), but right now it's not so easy - how can they confirm to the advertiser that the ad was seen? What are they gonna do? Put in a 700-character long link in the conversation?
I'm pretty certain that the ChatAI providers want to show ads, but until they can bill for it, they aren't going to.
At some point the billing will work, and then they will.
My point is more that thinking advertisement is simply "here's a coupon buy this thing" is naive. The more pernicious flavor is "this thing that everyone knows hurts you (but makes us money) isn't that bad. In fact it's good! You should do it!" That flavor is pervasive to such a degree that people don't even register it.
The AI people call this "alignment" or "safety".