Many of those providing answers are not reading the question properly. The question is "can the $3,000 be deferred, or is it mandatory for $3,000 to be included in the current year as an above-the-line deduction. In other words, if the standard/itemized and other deductions would be enough to offset income to be $0 taxable, can the entire capital loss be carried forward without applying $3,000 of the loss in the current year.

The answer to your question: in each year that an excess capital loss cannot be used to offset all capital gain, a minimum $3,000 capital loss must be considered (i.e., applied on the current year tax return as an above-the-line deduction). This would be mandatory, even in the case where other deductions (i.e. HSA, itemized deduction/standard deduction) would otherwise have offset taxable income to $0.

Even if after sustaining a capital loss in a particular year you did not file a tax return, in the subsequent year you'd have to reduce the available capital gains loss by $3,000.

Example:

In tax year 2020 you sustained a capital loss of $20,000. Your gross W-2 (box 1) income of $4,000 was your only income, with no income tax withholding and no estimated tax payments. Although without the $3,000 capital loss deduction your standard deduction would have reduced your taxable income to $0 (and therefore you would not have needed to file a tax return), you'd still have to reduce the $20,000 loss by $3,000 and would only carry over $17,000 to your 2021 tax return.

Consequently, if you'd been required to file a 2020 tax return, but other deductions would have otherwise reduced your taxable income to $0, you'd still have been required to apply the $3,000 capital loss as an above-the-line deduction and carry over $17,000 to 2021.