I’m aware that a single layer DVD costs only few cents, but is it really needed to trash a disc when something like this happen?
Until the disc is still readable there is no need to trash it, and there is no evidence that the disc can become unreadable after a short time.
In these situations I suggest to use a software like DVDisaster to make a recovery file instead of trashing the disc and increase the amount of waste in the world
The procedure is pretty simple and is described in detail here
IF the disc should become unreadable, then you can recover data and eventually burn again them on another disc.
Is it really a bad idea? A bit uncomfortable maybe, but certainly environment-friendly