re: Why does New Orleans have those shitty reflective traffic lights?

I'll try to explain....

Say you are crossing Washington on Broad...think there is one there.

While waiting to head west, the traffic on Washington is is headed North, and taking a left on to Washington (going in the same direction as you). They have to stop in the neutral area of the intersection due to the Southbound traffic on Washington coming at them.

Those neutral areas can hold 6-8 cars, and can't clear out until the Southbound Washington traffic has stopped.

So, they stop the southbound traffic with a red light, and give the green light to just the neutral ground. THIS is the stoplight that is in question for the OP.

Remember you are sitting on Broad looking at the neutral area. The "shitty" style light has allowed the area to clear out, while still allowing the northbound traffic to continue to flow.

After a set time the northbound Washington traffic is stopped with a full red and the usual traffic light green comes up to let the Westbound Broad traffic proceed through the neutral area that is now cleared.

TL;DR
There is a reason they are there. You cannot run one unless you ran the regular light as well.

FWIW, I think the light in question is Clearview and Airline...I think.