You are correct that if you do not itemize deductions, you cannot deduct the state tax allocable to investment income.
See the instructions for Form 8960, under Part II—Investment Expenses Allocable to Investment Income and Modifications. State, local, and foreign income taxes are deductible if properly deducted on your return when calculating your U.S. regular income tax.
If you don't claim a deduction for these taxes by itemizing, you can't claim them on line 9b of Form 8960.
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