With negative feedback, you would basically be changing the comparator to an operational amplifier that is trying to drive a digital output instead of producing an output that is proportional to the difference in input voltage. How this would affect an LED that is driven by the digital output is uncertain and very likely undesirable. Best case is the output would vary linearly with changes in input voltage.
Comparators, used to create a logic "1" or logic "0" digital output by comparing the polarity and magnitude of two analog inputs, are special forms of high open-loop gain differential amplifiers with digital output driving capability. The differential gain is large enough to cause the output to change states for very small (microvolt) differences between the two inputs. For this reason, any input with sufficient noise will cause the comparator output to oscillate wildly between logic "1" and logic "0" states when the differential input voltage approaches zero. This oscillation is an undesirable condition that can be prevented by adding hysteresis to the comparator circuit with
positive feedback.
Negative feedback is never intentionally used in comparator applications because it deceases the closed-loop gain of the comparator, which then increases the allowable difference in compared inputs that will cause a change in logic-level output. You typically want the comparator logic output to change only when the measured input is very nearly the same as the reference input, being a few microvolts more positive or a few microvolts more negative. Differential input voltages
between the limits that cause a change in output state should
not cause a change in output. This is an attribute of a comparator circuit that has hysteresis.
Hysteresis needs to be as small as practical to prevent changes in comparator output caused by noise on the inputs. If a typical open-collector comparator output is pulled up to logic "1" with a resistor, and the output at logic "0" is near ground potential, a largeish resistor can be inserted between the output and the "positive" input terminal to implement hysteresis. There needs to be a finite resistance to common on the "positive" input terminal for the positive feedback to be effective. Note that the designation of "positive" and "negative" for the two input terminals refers to the direction the output will swing, positive being toward logic "1" and negative being toward logic "0", when the differential input voltage has those polarities.
More information can be found on
this thread, which discusses using an LM318 operational amplifier as a comparator.