Sorry Matt but that's simply just not possible with CIC clients. 👀
And as Adriano mentioned just above, sometimes they don't even provide FTP access. So yeah, it might be a "dangerous" feature, but it really helped when debugging things without having to waste time getting the proper FTP/phpMyAdmin access.
I would very much prefer you guys slap a big fat error message (or something similar) above it so normal users are scared of using it rather than removing it altogether...