If an existing character, say a Fighter, decides to take a level of wizard with no prior mention of learning magic or interacting with wizards, and in a wilderness with no opportunity to find another wizard, would you let them go ahead?That's a slight exaggeration, but yes, I had a lot of 17 year old archmages during the 3e years. Most DMs don't advance time that much during campaigns.
That said, "hamstring the criminal background" is also an exaggeration.