Obviously the first two aren't the problematic ones. The issue is that an algorithm wouldn't know what distinguishes those from the third, obviously.

How about sleeping pills? Opiates? Local extortionist cult?

I think that algorithms, and AI specifically, are perfectly able learn what distinguishes those. Maybe even better than someone who might not be in their best state of mind.

The handwaviness is telling. Why would an algorithm or its creators even care about the difference? The highest bidder is the highest bidder.

Because the whole of Google's ad business stands on people wanting to click on the ads shown, and buy the products offered through them. That's why they spend resources on detecting misleading or fraudulent ads, which by your reasoning they wouldn't care about as long as they paid. PR is very important for this business to be sustainable: If the goal was for every user to click through one ad, and then never again, that might not even pay one engineer's salary.

What's misleading or fraudulent about those ads? Maybe you mean "morally reprehensible," in which case I ask where you draw the line between the morally reprehensible (auctioning off the method of suicide to a depressed person) and the morally questionable (say, auctioning off the final bankrupting car purchase to a financially irresponsible person)?

Detecting misleading and fraudulent ads is just an example of things they wouldn't spend resources on, if following your reasoning of "short-term money is the only thing they care about."

There's not only the "morally reprehensible" metric ("Don't be evil"); there's also the "absolute PR catastrophe" metric that printing such an ad for a rope would mean.