Legality aside, a lot of people are "trained" to respond to the 3rd brake light. It's a lot more obvious than the main lights in some scenarios, especially if you already have the parking lights on.
When my led brake light on my Infiniti was burned out and I couldn't find a replacement for a while, I noticed a lot more people would almost rear end me in traffic and then yell at me. When I fixed the third brake light, that all stopped.
So I would make every effort to keep my third brake light. I consider it the most critical.