They still have the means to manually calculate the weight/balance etc. Some (most?) airlines require the pilots to do a manual cross-check worksheet of the fuel, weight/balance and a few other safety of flight items, before they take-off. This helps avoids mistakes like over-rotation on takeoff etc.
One particularly amusing case was in a 767, where the Captain handed a copy of the worksheet to a young girl who loved math problems, and was travelling in first class as a VIP. The young girl found a mathematical error in the worksheet. It turned out the flight computer had the fuel CG incorrect by 2-3% in certain cases, and both were incorrect.
A quick call to Boeing, and 20 minutes later, fuel transferred and the flight proceeded.
I suspect the Southwest aircraft returning to the gate, was a procedural abort, than a safely-of-flight issue.
Add in probable regulatory requirements that are also implemented by software, and that probably makes it illegal to fly.