|If you are worried about the label coming loose the paper labels on the pre-labeled disks are fastened with some sort of adhesive. Still the possibility of them dislodging.|
I have used a CD Stomper for many years and have never had a problem with a label. I read where leaving that type of label in a car player could cause problems. In the summer, cars can get really hot inside. I don't see there being a problem with disks stored in a building. If you are using jewel cases you could just use the case label and forego the disk label.
If you are worried about long term archiving, you should be more concerned with the quality of the burn and the quality of the disk. Burning at the fastest rate may result in a playable disk that isn't burned optimally.
Optical burners use a variable intensity laser for both reading and writing. As the laser gets older it can become weaker, which results in shallower pits. The lens can also cloud up restricting the passage of the laser light.
There are separate lasers for CD & DVD media. I assume that holds for bluRay also. The wave length of a DVD laser is shorter, allowing smaller pits, which allows more pits per disk.
One other point to mention, I have a third party labeling program that allows you to place more information on the labels. I used to use it to label music CDRs and was able to place as many as 30 names on a label and still be readable. Very useful for archiving purposes.
Be sure to also set aside a new drive that is compatible with the archived disks. Down the road you may not be able to play them for lack of hardware.