Except this isn't true: the fallout of a nuclear detonation is extremely limited - their physically isn't enough radiological material in the warhead for it to be greater. Troops with chemical suits and respirators could safely operate in a zone which was recently nuked - in fact ground zero is likely to be less contaminated then surrounding areas, since the effect of the blast is to disperse material.
The problem, like all WMDs (weapons of mass destruction), is that they're of limited value against military forces. The distances a military force fights a war over are generally large, and they're mobile - or dug in. The effect of bombarding someone's lines with nuclear weapons though is that you might produce a few holes, but if you tried to advance through them you'd be immediately surrounded since you didn't completely obliterate them.
But they're of devastating effect against civilians, and civilian assets like cities which can be military objectives. Leveling a city rather then taking it is certainly an option, but if that was your plan all along then you could also just drop an ICBM on it - and at that point we're back to "the primary effect of nuclear weapons is making ICBMs useful weapons".
The casualties from a full-scale nuclear war between the United States and Russia were always estimated as "only" being in the hundreds of millions at the top end. But the subsequent famines from the destruction transport and distribution infrastructure, would be in the billions within 6-12 months.
Basically the issue is "tactical" and "strategic" nuclear weapons don't make much a distinction: if it's worth hitting someone's frontlines with a tactical nuke, then why not hit the military base supplying those lines with it? And that base is probably in a city with industry, so why not hit that instead etc. etc. etc.
I suppose another way to put it would be, there's a "hidden" escalation threshold we don't really talk about because no one's been stupid enough to do it: destruction of arable land. You would find that international opinion and weaponry would turn on any country very quickly if they were found to be deliberately targeting and destroying arable land as a policy of invading and denying resources to a neighbor (think literally "salting the earth") on a large, deliberate scale.
Which is all a way of saying, the issue with WMDs is that they're WMDs and WMDs all have broadly similar issues - namely that they will do far more damage to civilians then military targets, even without special preparations, and that they don't allow taking and holding territory. "Clean" nuclear weapons wouldn't change that.