Tea bags are wrapped, they have a special coating and the paper with the brand etc, with all this, the herbs are protected and their scent and taste are guarded against the light, dust, maybe bugs and other smells for some time.
Still, you should keep your tea in a good place for it because this coating isn’t bulletproof, and that’s why tea boxes and cans exist. In there you could mix all your teas, sure, but if you really want to drink tea the right way you should divide them because the aromas are very powerful and will easily taint nearby teas and you’ll end up with a mix from all your herbs.
What I’m trying to say is that if you have the possibility of keeping each flavor separately then do so, it will taste so much better.