Expect a new class of companies to spring up overnight that are dedicated to bundling transactions to avoid this new tax. For instance, I could make a single transaction to my broker that covered all of my expected expenditures for the month, and that broker would then disburse it to my payees, bundling it with funds from other payers to avoid the tax on the other end.

I am strongly in favor of a tax on all stock market transactions, though—anything to deter HFT, which IMHO has little societal benefit while externalizing a ton of risk.

Wouldn't work. Tax law can tell the difference between an individual transaction and bundled transactions. It's also the only area of law that allows for ex post facto changes to the criminality of acts.

Tax law already handles much more complex schemes. Admittedly nowhere near perfectly, but then this scheme being simple frees up resources for policing, and the tax code being much simpler makes it less easy to exploit.

Why tax the income side when you could just tax the consumption side?

Taxing consumption is regressive; Bill Gates can't eat that many more hamburgers than the average person.

Write everyone a cheque.

Taxing income is quite regressive too: it’s how people with nothing can survive.

Taxing income at a few % as this scheme intends is not regressive.

For simplicity's sake. All transactions are taxed equally, no way to evade it by making false or borderline claims about the nature of exchange, and no resource have to be wasted on optimizing or litigating them.