Why four payments at all
No employer is withholding tax on freelance profit, so there is nothing to stop the whole bill from arriving on April 15. The law closes that gap with Form 1040-ES: four estimated payments covering the tax your withholding does not.
The due dates are fixed - April 15, June 15, September 15 and January 15 of the following year. Four equal amounts that add up to the required total is the regular-installment method, and it is the plan this page prices. Paying the same figure four times is simple enough to keep, which is most of its value.
The schedule only appears when something is still owed after withholding. When the paycheck already covers the federal bill, the page says so instead of printing four empty rows, because a table of zeros reads like a plan when there is nothing to plan.