Such policy will, ironically enough, result in much higher chances of nukes actually being used, and used successfully. If the enemy gets to nuke you without getting nuked back, they've fucking won, and won big.
They don't.
Nobody wins in that case. Mutated dogs and other Fallout/Metro fantasy aside, MAD is still the most likely way humanity goes extinct.
But you've just said that nuking back is
verboten, you've destroyed the main assumption of MAD - that the enemy
will nuke you back! What if the aggressor country fully known about what kind of pacifists there are in control of nukes in your country? And you better believe they'll know about that, because that's why both NATO and USSR have been spreading pacifist bullshit propaganda across each other during Cold War - for that very small chance that the enemy will indeed become stupid enough not to nuke back!
And no, it'll be waaaay less than "half the world" in such situation. India, Africa and Latin America are not likely to be nuked in most scenarios which don't involve indiscriminate world depopulation due to being neutral players in NATO-Red Dragons conflict, and those already make about half of the world in population.
They also lost. Nuclear winter, radiation, economy getting fucked over, starvation, so on. Humanity will proably survive this way but we'd be blown back to medieval at best.
Nuclear winter happens only if you do counter-value strikes (i.e nuke the shit out of enemy population, igniting cities and producing firestorms), which are not necessary if you know that the enemy is a bunch of nuke-averse pacifists - you just do a counter-force one, leave enemy without strategic nukes to retaliate, then go through their military and cities at your leisure, while always having an option to obliterate whatever hard opposition you might have by the atomic light.
And radiation? Nuclear explosives produce remarkably little long-term radiation, and most of the fallout is only dangerous on direct contact (alpha/beta radiation). Ever thought why Hiroshima and Nagasaki are nowadays big, populated cities? It's because of that.
So yeah, while usually nuclear war isn't winnable, if you continue to insist that nuking enemy back is always unacceptable, it just might become like that. Hence why retaliation should always happen.