The battery may get warm.
The internal resistance of low drain cells is higher, so it will burn off some of the voltage inside the cell, which produces heat.
The wasted voltage is measurable as “voltage sag”.
High drain cells have low internal resistance, so they burn off a lower voltage inside the cell, producing just a tiny bit of heat.
Less voltage sag.

Due to voltage sag, the battery will not be able to provide enough output when it runs low on charge.
In practice this will probably be the only noticeable draw back.
But when you have a high power light (hard driven XHP50) and you run it for long periods, the cell may get hot.

What light are we talking about?