I believe that God's established guiding principle of "righteousness" (see
Psalms 89:14 & 97:2) demanded that He "tempt" Abraham. As someone has already noted, the word "tempt" literally implies/means to "prove." We find many instances within the context of the Bible wherein it is explicitly stated that God undertakes an act for the purpose of proving, trying, or testing the manner in which both mortal humans, as well as angelic beings, are subjected to a "testing" of His right of rulership over them.
In the garden of Eden, God "tempted" (that is to say, sought to test/try/prove) Adam's willingness to have God exercise rulership over him. We also find that chief among the reasons why the Israelites wandered in the wilderness for 40 years was for the purpose of "trying" them.
James was inspired of God to write and inform us that "The trying of your faith worketh patience." (
James 1:3) Peter also wrote to tell us: "Beloved, think it not strange concerning the fiery trial which is to try you, as though some strange thing happened unto you:..." (
I Peter 4:12)
These things only "scratch the surface" of the many things which could be written on this issue. I hope that the few that I have noted might be helpful in some small way.