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.
the "tax" part is obviously important (dividends are taxed while unrealized gains are free until security is liquidated). what most people ignore when doing these types of analyses is that a bird in hand is worth two in the bush: your risk of loss in the non-dividend payer is always 100% whereas your risk of loss in the one with the historical income stream is price - dividends received.
It's impressive you just looked this up on Wikipedia and grasped what the paper's authors who have PhD's don't seem to get.
Though maybe the authors know what they're doing and were under pressure to publish (publish or perish in effect?) so they just picked one of the more BS low-hanging fruit theorems in economics to poke holes in for the millionth time.
>> So basically the theorem is irrelevant, because none of those assumptions apply
I don't think its totally irrelevant. It may not be applicable in a today's real world, as you point out. But the point of a model is to try to explain what happens when you change the input parameters.
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.