It is of course possible that the BA bean-counters have got it right (from their, and the shareholders, point of view).
As noted above, the cost of a radical overhaul of BA's IT infrastructure is likely to be astronomical, and probably at least a couple of orders of magnitude larger than the cost and pain of a fair number of days of disruption.
It makes no difference to BA how many upset passengers swear never to use the airline again, unless it starts to make a big impact on the bottom line.