Earlier quoted context omitted.
As others have noted, the IRS doesn't know everything, and some things may be to your advantage to report to them. They could send you a bill and ask you to fix it, but many people wouldn't know where to look to find mistakes. For example: RSUs and NQSOs (employee stock grants) are in my experience handled extremely poorly by default. If I have RSUs vest when the stock is worth $10 a share, then I pay income tax that…
Wait, do brokerages report stock sales to the IRS?
> A broker or barter exchange must file Form 1099-B for each person: > For whom the broker has sold (including short sales) stocks, ... etc., for cash
https://www.irs.gov/instructions/i1099b
To elaborate on the GP comment, the issue is not whether the brokerage reports, but how they do it. You generally compute capital gain income as (sale price) - (acquisition price). If you buy a stock on the market and sell it, brokers generally report both sale price and acquisition price to you and the IRS.
But for employee stock compensation, the broker can report sale price without acquisition price to the IRS. If you don't report the acquisition price yourself, the IRS will think that it's 0, and assume your income is much higher than the real value.