You keep harping on this type of statement, but so far it lacks support.God intended the death of Jesus to atone for just His elect....
Now, that doesn't mean that a theory is necessarily wrong.
But, what provides the most Scriptural support should be considered as the most secure to the truth.
So far, a limited atonement for only the elect is terribly weak.
Better is admitting that the Blood shed was for all, and that the redemption resides completely in the prerogative of the Father.
At least that way there is the greatest amount of Scripture support, it violates no Scripture, and it is faithful to both the OT type and NT fulfillment.