"If Iowa had wanted to change its status to a slave state in 1847, how could the federal government prohibit it? Congress had no power over a state in this regard, and I see no mention of prohibiting any State from doing so in this law."

You know as well as I that not all things are written in black ink on white paper. The law of unintended consequences is always active and in play. Congress may not have had a legitimate power to prohibit the expansion of slavery into the territories, but they did anyway by establishing this 1820 compromise, by saying that above a that line those states would be admitted as Free states and those below as slave state, which by the way when it was finally ruled on by SCOTUS, was ruled to be unconstitutional.

So where would a slave owner looking for new lands and moving west go with his slave? He would go where the practise was limited to wouldn't he. How many northern slave owners moved south when those northern states banned the ownership of slaves? When New York and Pennsylnvania ended slavery in those states did the slave owners get paid for their slaves? Did all the blacks in those states suddenly become freemen? No those northern slave owners did not set their slaves free they simply moved south, or took their slaves south and sold them.

For example if California had passed a law in the past election that Marajuania would be legal for recreational use, and the rest of the country had remained "Marajuania free" States, where do you think that all the marajuania advocate would have moved to? Where do you think that all the manufacturers and suppliers of marajuania would have gone to do business? Do you think that the people of California would have ever repealed that law in the future had it been passed? The same thing was happening in the southern states. Slavery would have been easier to abolish in the south had it not been consentrated in the south.

When you put people into a box they tend to stay in that box, people tend to simply "go with the flow" rather than fight the current to swim upstream. I am still of the opinion that the practise of slavery was in fact perpetuated and furthered by the 1820 Compromise. That States like Arkansas and Even Texas would not have become Slave states had that not been the only way they could be admitted into the Union because of political decisions made in Washington.