I don’t think Metatron left Muriel on Earth just “to take care of the bookshop”. But why exactly?
To keep a low-ranking angel knowing about Gabriel’s story on Earth? Or to keep tabs on Crowley?
They are terrible at being a spy, but they already have…well, not a friendship, but still some sort of non-hostile relationship with Crowley, and Crowley finds them amusing and non-dangerous (and if Metatron knows about Crowley’s trip to Heaven, he should know it); yet they still are actually loyal to Heaven. And Metatron considers them to be “dim”. Can it be that he wants to use it for his own convenience?
We all are imagining sweet scenarios where Crowley looks after Muriel while they are learning about life on Earth and they eventually become friends, but what if this exactly what Metatron wants? So he could fool Muriel into reporting to him about Crowley’s movements?
I don’t think it would work as intended - it’s dangerous to underestimate the “dim ones”. But can it be Metatron’s initial plan?