If you are OK exercising battery connections, you only have to disconnect one terminal from the battery (not both). There is some sense in removing one, but no sense removing both.
Agreed it can be quick and easy if the terminals and bolts are in good condition, or recently exercised, greased etc. In general I think you are more likely to cause extra work/problems exercising battery connections though. Especially if you have to start the tractor to run hydraulics, or move it etc, that's extra work right there.
I don't disconnect batteries. I attach the welding ground to a good shiny area near the weld and go to work. If I was welding close to the engine, I would consider disconnection in case I touched the wrong item with the stinger.
I have been paying attention to this issue for appx 40 years and not hearing of problems. If computer systems were that vulnerable I think you'd have to worry about the alternator, and perhaps the ignition system burning out your computer too, which is ludicrous of course. Static electricity has to be a lot more common threat. Think about how many times a tractor is driven up to the shop, welded on, then returns to service (without disconnecting). If this was a problem there would be lots of posts stating it drove up to the shop then didn't start directly after the weld. And had to replace the computer. Never heard it.
I understand it's the common wisdom, but,,,,,,, never heard 1st-hand evidence that it's true concern. If I was welding on someone else's eqpt I would ask them if they want to disconnect the battery first. I would say I've never heard of problems but mention that its common to do so. It might be a CYA move that professionals must do to protect themselves.