I looked up the Modigliani-Miller theorem, and the first thing wikipedia said was "in the absence of taxes, bankruptcy costs, agency costs, and asymmetric information, and in an efficient market, the value of a firm is unaffected by how that firm is financed." So basically the theorem is irrelevant, because none of those assumptions apply. We do have bankruptcy costs, agency costs, asymmetric information, and an inefficient market.

I think more important than yield in low interest rate environments is that dividends are generally pretty reliable, as opposed to price appreciation, which is not. A long history of increasing dividends shows a strong underlying business model and history of execution. Furthermore, for mature companies, there is only so much money you can productively employ; retaining money that you cannot use effectively reduces shareholder returns. Conversely, you shouldn't be paying dividends if you are entering an Amazon winner-take-all market because you need it to grow. So you really should care about dividends.