Frosts plan was fine it worked. And taking into account that at the time there was no future for mutant it was one option.
But if Scott wanted to chop Callahans head off then he should have decided that at the start.
Also given that they had access to the Avengers it probably would have been a good idea to ask Tony for help removing the bomb. Then gave them the vaccine to disperse after all.
The writing is all over the place