The dividend irrelevance principle is not a reason for avoiding dividend paying stocks, only a warning against buying dividend stocks with the misconception that the dividends add value. What is important is the ability to generate value from which dividends can be paid: Dividends are the distribution of value, not the generation of value. Indeed, research has shown that dividend paying stocks are, on average, value generators with the earnings they deliver.
An investor who receives dividends and who doesn’t need the cash for living expenses can simply reinvest the dividends to recover the value lost from the drop in price. Indeed, many firms have dividend reinvestment schemes where the dividend is reinvested back into the same firm. Of course, as with any investment, check that the stock is not overpriced (with the fundamental analysis in this book) before you buy it with your dividend. If it is, you might take the dividend and create a further dividend for yourself by selling the stock.
By the same logic, an investor who needs cash for living expenses need not buy a dividend stock, particularly if she sees not much value generation in that stock. She can buy a non-dividend paying stock and create her own dividend by selling part of her stock holding when she needs cash. This has the same effect as the firm paying a dividend: The price of her holding drops but she has the dividend equal to the same amount.
Both these cases are homemade dividends. They amount to the investor creating her own dividend policy, making the dividend policy of the firm irrelevant.