I don't think most ammo is valuable enough to store in big quantities in a gun safe.
A locking steel "cabinet" should be secure enough, and you can still use a dehumidifier in there if you want.
Normal ones should hold about 150 lbs. per shelf, if the weight is evenly distributed. You could always use a couple of 2x4s and give each shelf a center support, and beef up the sheet metal edges on which it sits, if you want to really load it up with heavy ammo.
On the other hand, a cheap gun safe can be found for just a little bit more than a sturdy all-steel locking office supply cabinet, so why not get the safe?
Well, maybe you'd NOT choose the safe because unless you want to spend $800 or more, it's going to be a lot smaller than a locking office supply cabinet. Compare the volume inside each one.
What is your reason for wanting a safe?
I've always been under the impression that storing ammo in the cardboard box they came in stored in an ammo can is pretty safe. If you are concerned about moisture you can always vacuum pack the ammo in plastic bags
If you want to secure ammo, get a locking mesh front cabinet or light metal locker where pressure won't build up if it starts blowing up from fire exposure. Loose ammo going off outside of a gun barrel is pretty anemic, but a tightly sealed metal container full of pounds and pounds of gun powder is a bomb.
I don't think modern small arms ammo is going to blow up en masse, even in a gun safe or other closed container, the same way that much loose gunpowder would.
Small arms cartridges do not detonate each other. If you line up a bunch of them together, pressed firmly against one another, and cause the middle one to go off, the others won't detonate. They'll just be knocked over or blown away, but still holding together and containing their own propellant charge.
The term is "sympathetic detonation." I don't think that ammo will do this, even if stored in a closed container that holds in the pressure (briefly).
Will the rounds cook off due to heat? Sure, they eventually will pop. Like popcorn-- each round will go off at its own distinct time, and only rarely will more than a few kernels pop at the exact same instant.
Now, if somehow you could cause thousands of rounds in a gun safe to detonate at the exact same instant, THEN there'd be trouble, and having such a safe door shut with a good tight seal would probably make the "giant pipe bomb" mentioned above.
About 10 years ago I had my duty truck burn in my driveway.
In its steel cross bed toolbox I had about 500 rounds of 45 acp with 10 cases of road flares next to them. The fire was rapid and intense. But the rounds went off ,as Gunsmoker described it, like pop corn. I think it would take a lot of effort to detonate a cashe of ammo all at once.