Example calculation for a single person in Zurich as I understand it:
Expected deductions: 9’000 (0.3% for asset management) + 2’600 (health insurance)
Taxable income: 70k - 9k - 2.6k = 58’400
Total income tax: CHF 6’586 => Tax rate 11.3%
Total wealth tax: CHF 11’362
US WHT: 15% of 70k = 10’500
Taxable income from assets: 70k - 9k = 61’000 (dividends minus asset management)
Swiss taxes for income from assets: 61’000 * 11.3% = 6’879
That’s the maximum that you can get back via DA-1, which is lower than the 15% in this example. There is an additional cap which is the total income tax in Switzerland, which is slightly lower in this case (due to the health insurance deduction and no other income). You’d only get CHF 6’586 = 9.4% back in this example.
In total you would pay CHF 21’862 in taxes, CHF 10’500 in the US as WHT and CHF 11’362 (wealth tax) in Switzerland. Depending on the share of US stock in the 3M, (partly) switching to Ireland-domiciled ETFs would be better for you and Switzerland (I haven’t done the math on that).
See also https://www.estv.admin.ch/dam/estv/de/dokumente/vst/merkblaetter/da-m.pdf.download.pdf/da-m.pdf