Why don't Aedra dabble in the affairs of men? Is it simply part of the pact they made, is it principle, or is it some other reason? Where do they exist, and can they even reach Mundus?
The current state of the Aedra is abit, odd. Of those that didn't die or degenerate into the Aldmer, most either left with Magnus or departed following the Convention:
"After these two acts, which is commonly called the Convention, the gods left the earth."http://www.imperial-library.info/obscure_text/nu-hatta_nu-mantia.shtml#5
The Convention refers to the period just after creation spanning the arrival of the Adamantine Tower, through the war with Lorkhan, and the creation of Red Mountain. This is the first half of the Aedra's story, of them creating Mundus and dying/procreating/becoming earthbones/departing to Aetherius.
The second part is here:
"The people of et'Ada believed for so long and so well, that their beliefs may, just may, have drawn upon the energies surrounding Tamriel to bring the gods themselves into being. If that is so, the conflict between the Light and the Dark provided the energy, and the et'Adans the structure, that created the gods of Tamriel."http://www.imperial-library.info/dfbooks/b055_lightdark.shtml
The gods create man, and man recreates the gods.
So, the Aedric interaction with Nirn is a result of its interaction with them, they get legitimacy and power through worship and belief. However you can't say that the Aedra don't dabble in the affairs of men unless you just haven't been paying attention. What do you call the end of Oblivion? or the avatars of various Divines in Morrowind? or the blessings of the alters and wayshrines? Or the wind, the rain, the fact that time works in a linear fashion? All these are the Aedra being involved. They exist both as part of Mundus, in Aetherius, and as part of myth which due to the nature of the universe is just as real as the ground you walk on (which coincidentally could be seen as them as well).