If the principle is "Tax level should consider both income and wealth", which I agree with, then we should look at what's a reasonable level of taxation for billionaires with no taxable income, not get hung up on child credits.

If the principle is "Things like child tax credits should have a special limitation against billionaires", then I disagree with it, well, on principle. Tax system should be simple, not complicated. Having a complicated tax system is what benefits unscrupulous billionaires because then nobody can figure out exactly what they're paying and what they should be paying. Also, maybe it's just me, but the argument sounds disturbingly similar to "People buying latest iPhones don't deserve welfare checks!" - just in the other direction.