I understand that read-only mode prevents further writes, but can't a burner just ignore that and burn over the original data anyway?
Yes, if you modify the firmware on the burner then you could do that.
That means either having access to the firmware's source in the first place (read: support from the manufacturer) or some tricky manipulation.
I know you wouldn't really be able to store any new data on the disc because it would most likely corrupt everything,
Correct. Once CD-R or DVD-R (not -RW) is written to, part of the disc is physically changed. There is no way to revert this.
For more details please see this post: What prevents CD-R from being rewritten?
but for data-destruction purposes, what's preventing this?
Nothing but the safety checks in the firmware.