I like the idea very much. The shockwave tearing through the planes, killing gods, etc would give a handy opportunity to thin out the normally expansive FR collection of gods. Love the idea of the neutral merging of Mystra and Shar.
Probably make interplanar travel to planes that don't directly overlap the prime (ie planes other than the border etherial) much more difficult, maybe near-impossible. Could help nip any 'giant tide of demons, flowing in' ideas in the bud. Outsiders that were present on the prime when the apocalypse happened could be stranded there.
If you want to cut down on the divine casters overtaking all, thing - maybe make most lay clergy in the years following the apocalypse be members of the Expert class, rather than Clerics - and the ability to actually channel divine magics a rare gift. Druids would be comparably powerful, as their spellcasting doens't stem from an extraplanar source.. but druids are normally pretty secretive anyway. Possibly even moreso after the events that fried the weave - they've got much bigger and more important things to take care of than Joe Dirtfarm's broken leg. They're busy watchdogging the world, making sure the things certain gods took care of before.. mountains.. the sea.. animal life.. don't just crap out on their own.