Was the warning from the angel to not look back solely a test of obedience or may there have been more of a reason? Ex.33:20 says “You cannot see My face, for no man can see Me and live!" God (Son of God) is seen in veiled form in His interactions with Abraham just prior to this. When veiled, He is able to be in the presence of fallen man. In Gen.19:20, Jehovah (God in His glory, not veiled) authors the destruction. "Then the LORD rained on Sodom and Gomorrah brimstone and fire from the LORD out of heaven". Could it be that God's presence was going to be manifested and the warning & judgment were in relation to Ex.33:20?
God punishes people for one reason: disobedience.
And there came two angels to Sodom at even; (Gen 19:1)
I will not debate the question of what or who is an angel. For the purpose of this answer, let us assume that whomever these two people were, they had authority.
...the Lord hath sent us to destroy [Sodom]. (Gen 19:13)
After all the shenanigans in Sodom, the angels decided it was time for Lot to leave, and leave quickly. They gave him some last instructions:
And it came to pass, when they had brought them forth abroad, that he said, Escape for thy life; look not behind thee, neither stay thou in all the plain; escape to the mountain, lest thou be consumed. (Gen 19:17)
There are the commandments and the punishment for disobedience.
- Do not look behind you.
- Do not stay in the plain.
- Escape to the mountain.
Lest thou be consumed.
Lot negotiated a bit, being old and not believing he could live through the run to the mountains, and the angels agreed the he could flee to the town of Zoar instead. They actually arrived.
The sun was risen upon the earth when Lot entered into Zoar. (Gen 19:23)
It was then that Lot's wife made a choice. She choose to disobey, and she was punished for it.
But his wife looked back from behind him, and she became a pillar of salt. (Gen 19:26)
Why Lot's wife looked back is a completely different question.
Why looking back was a big deal is also a completely different question.
But why Lot's wife was punished for looking back is explained in scripture. She was commanded not to, and told she would be consumed if she did. She disobeyed and received the indicated punishment.