As a couple of others have already pointed out, the reason is that diodes (except for some special cases where there's an external source of energy from light) don't work as a power source in a circuit, whereas batteries do.
I'll expand on how you can see that is true.
First, you've probably already seen the power formula:
P = IV
Power is the product of current and voltage. But both P, I, and V are all signed quantities. The meaning of positive or negative P is based on a common convention: When P is positive it means the circuit element is absorbing power, using it to do something useful (like emit light if it's an LED or turn a motor) or just turning it into heat (as in a resistor). When P is negative it means the circuit element is delivering power to the rest of the circuit.
For this convention to work, we have to be careful about how we define the direction of I and V:
If we define the positive terminal arbitrarily, and say that the voltage is positive when the positive terminal is at a higher potential, then current is positive when it goes in to the the positive terminal.
To the point, the power flow is into the device when current flow is into the terminal with higher potential.
If we look at a diode in comparison to a battery cell we see that the relative directions of current and voltage are opposite:
In fact, in a circuit theory context, we would say that the current through the battery is negative. In day-to-day use we rarely make this distinction, because everyone knows which way the battery current is meant to flow, although there are certain manufacturers (NXP?) who carefully observe the circuit theory sign convention in their datasheets.