Can someone explain the myth of dividend income, if your account value does not go up from dividends?

Stock A: $50, and pays no dividend

Stock B: $50. Tomorrow it pays $1 dividend. So, tomorrow stock is $49 and you have $1 cash. (Edit: Yes, On the ex-dividend date, the price of the stock drops by an amount equivalent to the dividend. That is how dividends work)

In both cases, you still have exactly $50. I do not see magic free money income that everyone implies dividends create. I see no difference between dividends and simply selling $1 worth of stock. In both cases, you still have exactly $50. Can someone explain what I am missing? Dividends seem like the biggest myth in investing history because dividends do not increase the value of your account.

Edit: People say that stock B can go back up from $49 to $50. Yes, but stock A can also go up, just the same. No different than if stock A simply went up $1 from $50 to $51. Same thing in the end. In both cases, you have $51