It's actually the opposite. Zelle and the banks couldn't be tighter.
Zelle is owned by Early Warning Systems (EWS). EWS is owned by an oligopoly consisting of most of the large US banks. EWS is also what those and a majority of other banks use for screening and monitoring customers. They're essentially the banking version of Equifax, Experian, and TransUnion; keeping track of countless transactions people engage in daily—especially those that they consider problematic. And just like the big three credit bureaus, everyone has an EWS "score" based on their banking history, and the lower the score the higher the chance of getting locked out of something as basic as access to banking.
Any time something "negative" happens with a customer, whether it be a bounced check, overdraft, suspected fraud, account freeze or closure, lien/levy/garnishment, and a whole bunch of other factors, it's recorded on their EWS report just like when someone is late with a credit card or loan payment. Even seemingly innocuous things like ordering checks, putting a stop payment on a check, or accidently transposing a number on a deposit slip or mobile deposit are often reported since they might indicate that person is a criminal mastermind instead of someone who simply needed more checks, or had a check get lost in the mail, or forgot to put their reading glasses on when making a deposit.
If one bank closes an account because of any of these "negative" events (especially if an SAR is filed), the domino effect often starts and other banks will usually refuse to let that person to open a new account for 5-7 years, and existing accounts at other banks that subscribe to EWS often end up getting closed as a precaution.
Zelle being balls deep in the middle of all of this also reports the same sort of activities to their loving parent company, so if they close an account, suspect fraud, or take any other kind of negative action against a customer, not only is the bank connected to the Zelle account aware of it, but every other bank that the person does or might attempt to do business with is as well.
Bottom line: never use Zelle. For anything. Not peptides, not paying your sister back for pizza. Sending cash in the mail, or sending a Western Union is probably a safer bet and less likely to have as wide-reaching unintended consequences.