We can put this to a simple test if it is ethical or not, does the choice follow one of the two main moral theories, Utilitarian or Deontological?

To get the easy one out of the way it can not be deontological because the WOL makes an action for many souls and doesn't ask them all. This also would never work for we know the WOL doesn't work on this moral framework since under it all murder is wrong and the WOL does kill people. Without going through all of Kantian Ethics in detail the very notion that the WOL did this action without consulting everyone this action was done to first makes it a clear case it was not moral by this framework. Though the WOL has never used this moral framework this should not surprise anyone leaving only one other means.

Under the utilitarian framework, we look to see if this action created more good than it harmed, the outcome judges if it's moral or not. so did turning off the souls make for a better outcome for more souls in the universe? Since in FF14 people are judged by having souls or not as being alive it would be measured if turning off the Endless and stopping the need to consume more souls to keep it going saving more souls or harming more souls. It seems by the fact that they need to drain the source to keep it going longer that stoping it needs to happen as the Endless need souls to keep going and keeping things as they are means the Endless are going to consume more and more souls. Putting an end to it means stopping more souls being used for fuel in the future so that could be argued as a moral outcome. WoL has always been one to weigh the options of outcomes so a utilitarian framework seems appropriate.

So if stopping the Endless is an over all better outcome for more souls then letting things continue then the WOL is moral.