LED chips are designed to run efficiently at a specific (sometimes fairly narrow) range of current, and have a specific upper maximum current that the LED can handle without excessive internal chip heating. I assume most LED lights run their LED chips at or near the maximum current for peak brightness without excessive heat losses.

How the maximum current is controlled varies with the lamp design. On the 12 volt LED strips there are segments with each segment having three LED connected together in series with a small resistor. The resistor provides current limiting when the strip is powered by 12 volts.

A little more than 12 volts will increase the current through the LEDs and increase the brightness. A lot more voltage applied to the strip runs the very real risk of cooking the LEDs and/or burning up the resistors.

On some small battery powered LED lights the batteries are directly connected to the LED chips with just a switch. The only current limiting is the internal resistance within the battery and the battery output voltage being a close match to the voltage needed to run the bare LED. Raising the feed voltage could easily overdrive the LED.

Some LED lights have actual electronics to control the power delivery to the LED chip(s). These lights tend to be higher priced and high performance LED gear, such as high output LED flashlights.