Overall I think this change is excellent. However, I want to see some extra safety added:
all the user has to do is check a box to confirm they understand and then click the big button at the bottom to delete their profile. That's it!
Currently that means I just click these three things and my account's gone:
In general, close-proximity link clicks leading to a decision as consequential as this one make me a bit nervous. I've wound up clicking more things more times just fumbling a tablet in my hands while changing seat on the train.
Some utilities involve extra confirmation from another factor than just clicking. For example, World of Warcraft has you type in your character's name before you can confirm the deletion. Some other services have you write out "I AGREE" into a text input field or something like that. In any caseWhatever the method chosen, a process like that leaves virtually zero chance of anything happening accidentally, and makes it an extremely deliberate process.
I also think Monica Cellio's suggestion to add an email confirmation definitely should happen, and not be an option but a default step in the process.
If you implement requiring someone to re-authenticate (i.e. type in their password), that shouldn't be the text box in and of itself -- autofill will often make sure that's one less thing to interact with, not one more thing, defeating the point of making sure you're doing this deliberately.