A safe seems like a great idea for storing everything in your home that is irreplaceable, and for important documents and jewelry it certainly is.
Since your videotapes are irreplaceable and priceless you might be tempted to store your tapes in a safe as well and I certainly can’t blame you for wanting to make sure they survived a disaster.
The problem with a fire proof safe is that there is no air circulation and any moisture in the safe stays contained inside.
I’ve seen hundreds of tapes (most commonly 8mm/Hi8/Digital8) that were stored in a safe and became damaged by humidity exposure. Over time the lubrication on the surface of the tape starts to break down and starts to stick to itself, causing the tape to break when playback is attempted. Most tapes that are exposed to this kind of damage can be repaired, but the best solution is to avoid it in the first place.
If you want to store your tapes securely make sure to air out your safe on a weekly basis, look into disposable desiccants or use a special media/data fireproof safe that is designed to prevent humidity build up not just during a fire, but during normal conditions as well.
If your tapes have been exposed to humidity inside a safe (or out!) and no longer play, don’t worry, chances are very good that they can still be repaired!