I don't want funds that pay distributions whether cap gains or dividends. But I think that is also impossible to achieve. All funds that I own will pay dividends, but the cap gains distributions are rare and small.
I prefer to have funds that pay dividends that are 100% qualified ordinary dividends as opposed to any fraction of non-qualified ordinary dividends.
I prefer to control when I realize capital gains. Furthermore, I have lots of carryover losses that can be used to offset any realized capital gains that I create. Because my taxable funds don't pay unnecessary cap gains distributions, I have not been using up those carryover losses very quickly. I do use the $3,000 of losses allowed to offset ordinary income such as non-qualified ordinary dividends.
So I don't need an automatic income stream because I can create a manual income stream that consists of return of capital (not taxed), qualified dividends (taxed at 0% or other favorable rate), and realized cap gains (offset by carryover losses).
Return of capital is not even reported on one's tax return, so that's the best kind of income to get and may be even better than a Roth withdrawal which is also tax free and does not contribute to Adjusted Gross Income.