Only Wizards can get Shovel permanently, by scribing the scroll before casting it. Then again, a Warlock can get the exact same Familiar through pact of the Chain, just not with the funny lines.
Wizards and Sorcerers can get Shovel permanently.
You don't have to scribe the scroll to permanently get Shovel. Just go through the dialogue with Shovel, and I think the key is you have to ask "is that what you and your master did?" when it gets to that point in the conversation.
Then, when you initiate conversation with Shovel a second time, Shovel will call you a "spell shite," and you'll get the ability to summon Cheeky Quasit for free.
Note: this doesn't work for storm sorcerers, and it doesn't work for some reason if you play into the conversation about teaching Shovel to be a dragon.
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Regarding the illusionist, I find the subclass features disappointing. These are the kind of problems I have with DnD in general. I don't like the way there are clear better choices between subclasses. In my opinion, it should be worked on across the board, system wide.