If Sherlock doesn’t understand his emotional context (that he and John are in love), he will not get his Three Garridebs moment
If Sherlock doesn’t find his emotional context The Three Garridebs will die (TFP). And if Sherlock doesn’t understand that you have to take your shot at love before you miss it (TLD) he will not get to have his Three Garridebs moment with John. This is the same theme brought up in two very different ways: love with complete you as a person but you gotta get in the game, you got to tell the other person who you feel. Sherlock has to face his feelings to get a chance at romance with the man that he loves.
As harsh as I originally saw the scene where the three Garrideb brothers die, I know see it as a cautionary tale for Sherlock. Eurus is his innermost hidden feelings. His love and his fear of love.
It is Eurus as his true, ‘emotional context’, who keeps pushing him through all of these increasingly difficult challenges. And even though he makes the right deduction, Eurus doesn’t play fair and his symbolic love confession (the three brothers) die.
By the end once he’s figured out how to save Eurus and added, ‘I am lost without your love’, to the deduction we see that he finally understands his emotional context. (Thanks to @writemeastoryofsolitude for that excellent meta).
Then we get him back together with John, as before, as if they’re a couple. Hopefully, though, we still get our proper romantic Garridebs moment where he finally tells John that he loves him.