If I had a personal account from my wage earnings and handful of profitable trades at Wells Fargo, my modest account would be reasonably protected through mandatory insurance and I would know that because of the FDIC sticker on every fricking window and website.
On the other hand, if I managed a large liquid asset portfolio and I considered having Wells Fargo provide banking services, I would know that my deposits would not be implicitly insured and that any substantial deposits were more like a loan to the bank, subject to their own illiquidity and insolvency. Because that's how banks work, except for the specific carve-out for small accounts. Thus, I would practice risk management suitable to my needs by vetting my bank(s) practices, diversifying my holdings, buying private insurance, or just hiring a professional who I could entrust to manage those things for me. Thankfully, because I have a large liquid asset portfolio available, I can afford to do that.
So at the end of the day, any large deposit I make with Wells Fargo is actually a risk-laden investment that I've made a calculation to play, just like that equity share that you bought on the stock market.