Walking around with 100 000 lumber in the pockets makes much more sense.
Well yeah, just like walking around with a shotgun, AK-47, grapple rope, hammer, wrench, knife, and rocket launcher does.
Thing is, if you're walking around with a ton of stuff on you, it's fair enough to say that your player can hold tons of stuff because it can easily be lost.
Letting someone store tons of stuff in a safe isn't necessarily a good thing, because now instead of having to compromise what you're going to carry on yourself, etc, you can just store all of your stuff in a safe.
So when you think about it, infinite safes does detract from the gameplay a little bit.