That's about the business implications, not about moral ones as the comment I replied to was asking about. Completely different argument.
You're thinking about this as if the question is simply about whether or not payment processors should have the job of examining every individual payment. There's a potential discussion to be had there, but that's the only dimension of the topic, and one of the things we're talking about entire classes of activity.
If prospective clients like "Assassination Central" or "Doordash Blowjobs Inc" approach you as a payment processor, you might have some idea of what's going to happen. And in general payment processors have both an incentive and regulatory obligations to understand what kind of business they're facilitating, not to mention whatever individual inclinations they might have.
When it comes to something like Venmo, I'm not really sure how to handle that. I suspect invasivity isn't the only issue, it's also probably practically difficult to police effectively, but at the same time, if there were means by which reasonable correlations could be made, it's not clear to me that there's no activity whatsoever for which there's a case for flagging, however controversial which cases meet that criteria might be.
Should it be illegal to start a vegan payment processing company that won't allow butchers to be paid through them? If so, then why should it be illegal?
Does postal system open every envelope to see if there is cash inside sent as an illegitimate payment to someone? Because it's easier to do it online should not be the base for justifying it.
Would you be happy if your email provider scanned all your emails using ML systems to detect illegal activity? For some reason we value the privacy of our communication more than other types of transactions.