Your question doesn't have an answer. With rates this low, how much are you making on the high-interest account? If you're making money at a trading account, you should easily make a higher return than any bank account.
This is all long-term by the way.
I call it "buy and pray." It's trading without a stop loss. It's for amateurs.
Stocks go to zero all the time. Sometimes the company even stays in business after that. Boston Market is a famous example. It went from $50 to zero, even though there were still franchises everywhere. It turns out the stock was the business of selling to the franchises, and not the actual franchises themselves. CMGI is another great example. In the late 90's, people said CMGI "owned the Internet" and could never go out of business. The stock went to something like $300. Then it went to about 30 cents. I had one client who refused my advice to sell when the stock was still in triple digits. He lost everything.
You can enter "stop" orders that protect you somewhat. But anything you hold overnight is subject to the risk of "gapping" up or down. Let's say you buy a stock for $50, and do the smart thing of entering a sell stop at, say, $40. You will *probably* limit your potential loss to only $10 per share. But what can happen is that really bad news can come out overnight on the stock. It can close one day at $50 and open the next morning at $20. Provided your stop is a market order, you will get stopped out at the open with a $30 loss instead of a $10 loss.
Based upon what you've said, you should probably just avoid the stock market. Trading is a business, more so than it is a way to make cash for another business.