Hi Cassandra,  In the book of the City of Lost Souls, Simon, with the help of Magnus, invokes Raziel. He just uses an invocation spell, so if the Angel can be invoked with a spell why we must have the Mortal Instruments? Why doesn’t Valentine use an invocation spell, but instead looks for all the Mortal Instruments?— tessadriana

Magnus explains this in CoLS:

“There’s a reason the ritual of the Mortal Instruments was so complicated.” Magnus made the sugar bowl float over to himself and dumped some of the white powder into his coffee. “Angels act at the behest of God, not human beings—not even Shadowhunters. Summon one, and you’re likely to find yourself blasted with divine wrath. The whole point of the Mortal Instruments ritual wasn’t that it allowed someone to summon Raziel. It was that it protected the summoner from the Angel’s wrath once he did appear.”

The Mortal Instruments aren’t the only way to summon an angel. They protect the summoner from divine wrath. The Mark of Cain is the only other protection we know of that was able to fulfill the same purpose:

“What happened in the pentagram, with Azazel, made me think,” said Simon. “You said summoning angels is more dangerous than summoning demons, because they might smite down the person who summoned them, or scorch them with Heavenly fire. But if I did it …” His voice trailed off. “Well, I’d be safe, wouldn’t I?”
That snapped Magnus’s attention back. “You? Summon an angel?”
“You could show me how,” said Simon. “I know I’m not a warlock, but Valentine did it. If he did it, shouldn’t I be able to? I mean, there are humans who can do magic.”
“I couldn’t promise you’d live,” Magnus said, but there was a spark of interest in his voice that belied the warning. “The Mark is Heaven’s protection, but does it protect you against Heaven itself? I don’t know the answer.”
“I didn’t think you did. But you agree that out of all of us I probably have the best chance, right?”

Having Simon summon Raziel was a complete gamble, but it was one that worked out.

Dean took the angel who he’d allowed to possess his brother, because he couldn’t fathom a world where Sam was dead, and tortured that angel until Gadreel was unconscious.

Unconscious.  What kind of trauma would an angel have to endure before they blacked out?  Especially considering that in the past we’ve seen that hitting an angel causes more pain to the fist than the angel.  Can Dean cause that kind of damage because of the Mark, because somehow it burns strength into his arm?  Or is his pain, his anger, his addiction so strong that he has to let it out in a violent, bloody outburst?

Dean took the angel who possessed his brother, chained him up, tortured him, and listened to him beg to die.  He took the angel who reflected back to him all the worst parts of himself, the parts that are scared of abandonment, scared of doing the wrong thing and facing Dad’s retribution, scared of losing his place in the world and so he possesses Sam against his will; he took that angel and tortured him, and when that angel begged to die, Dean didn’t let him.

Dean didn’t kill Gadreel because he wanted to punish the angel, punish himself, punish them both.  Gadreel tells him all the things that he’s already telling himself, that Sam doesn’t love him, has never loved him, that he isn’t worth loving, and Dean uses the wrath of Cain to torture him until they’re both lying on the ground, beaten into shells of what they were just a few hours before.  Dean doesn’t kill Gadreel because Gadreel wants to die.  What he fears is living trapped for an eternity in chains.

Dean wants to die, but what he’s done to himself instead has condemned him to an eternity trapped in Hell.