I can buy my own stocks through sites like e-Trade and Schwab and Fidelity. I do my own banking with the bank's web site. Why do I have to buy annuities through a broker (human being)?

I’m pretty sure some annuities you can buy direct from the insurer and not a broker. Have you tried going directly to the company website that you are interested in buying from? Maybe the annuity you want in particular is only sold through salespeople or brokers. I think some annuities always carry a load and are only sold through some sort of salesperson.

No-load annuity.

https://www.investopedia.com/terms/n/no-load-annuity.asp

There are some no-load annuity contracts you can purchase directly. You’ll need to do some research, however, to identify them. Because annuities are insurance products, they’re generally sold through intermediaries.

Do the research; you can buy annuities on your own.

You may think you are buying stocks directly, but you are buying through a broker when you use their website. When you buy something “commission free”, it is because someone is paying for your order flow.

And depending on what you buy, you may pay a fee or it comes out of management fees for the product you buy.

When you buy a mutual fund, you still pay management fees; they may be explicit or they may be hidden.

And when you buy a CD from the bank, your funds are locked up for a term and the bank gets to play with your money.

Even sophisticated hedge funds pay management fees. Hedge funds usually run on a 2 and 20 basis.

A very common phrase on Wall Street is TANSTAAFL – There ain’t no such thing as a free lunch.