The center brace on your tanks are there for a reason and should never be removed for any reason. In doing so can result in total tank failure. Your tank will start to bow out both front and back.
How the tank lasted for years and years without failure in my strong opinion was pure luck!
I wouldn't chance it. Think about all the time,money invested in your tank then think about your fish and top it off with ruining furniture,floors etc....
Not worth it. You may think there doing nothing but they are. They are a very important part of the tanks design.
If your fish aren't dieing and they're healthy and happy, don't change anything drastic. I'd call removing the center brace a drastic change and strongly advise not to change the structure of the tank.
From a physics perspective, that brace prevents the two walls (front and rear) of the tank from bowing out from each other and is absolutely essential on a tank larger than 30 gallons. Even with tempered glass, it still bends when water presses against it.
Again this is JMO for what it's worth.
"When creating an aqua scape, strive for the beauty of imperfection, as its art and there is no wrong or right, it's left open for interpretation" James Findley