Why may not nations (even if they aren't friendly with each other) declare an all-out war against ISIS and its allies?
You may not remember an all-out-war. There hasn't been any involving superpowers for 70 years.
All-out war means lots and lots of people dying. And these aren't theoretical people. They are actual real-life, flesh and blood people, being killed painfully and gruesomely: bleeding out, with shrapnel wounds, with body parts missing. They are not all "bad people" they are people like you.
All-out war doesn't mean a few smart bombs, it means people like you being drafted and sent overseas to do or die.
And at the end of it you are left with the seeds of the next war. Get rid of ISIS, but there are other groups. There are other people who will take advantage of some regional instability.
The twentieth century saw two all-out wars. Let us hope the twenty-first will have two fewer.
After the devastation of World Wars I and II, and the beginning of the nuclear arms race, governments came to the conclusion that full-scale war was simply too economically damaging to justify its goals. The only victories in modern war are pyrrhic victories. So through the Cold War and beyond, major industrialized nations have restricted themselves to bush wars (small-scale proxy wars between puppet states), peace-keeping missions (efforts to stop internecine violence within under-developed nations), and incursions (limited-goal strikes against specific targets, now mainly accomplished by drones). Small wars can mean big business in arms sales and supplies; big wars would destroy too much to be viable.
This question seems fundamentally flawed in its premise.
There has been pretty much an all-out war on ISIS, within the limitations imposed by its structure.
Western countries have had a large coalition bombing and attacking their infrastructure and camps. Numerous countries have participated: USA, France, Canada, among others.
Iraq and Kurdish areas have fought hard on the ground to expel them from their territories.
Arab countries fought them. One of their atrocities was burning a captured Jordanian pilot.
Russia has attacked ISIS in Syria, though some of that is also muddled by their support of Hassad: a number of rebel groups have a radical Islamic ideology, so would be targeted regardless of ISIS affiliation or not.
Iran (Shia) fights them as they are Sunni.
Now, regarding the all-out war aspect:
ISIS, even in its caliphate-territory phase, was an amorphous organization with ill-defined borders and irregular troops. It has embedded itself in civilian areas.
During some of the final battles for their strongholds, in places like Raqqa or Mosul, it was an overriding concern to limit civilian casualties as much as possible. This isn't just about being nice - civilian deaths fuel insurgencies. On the flip side, ISIS aimed to get as many people killed as possible and wanted to keep their human shield.
So you may not have seen "carpet bombing" or the like and retaking ISIS-held cities seemed to take forever. But the fighting was nevertheless intensive by all metrics (and a large number of civilians died).
In short, pretty much everyone did what they could to get rid of them. No nation state has, to my knowledge, allied with them. The fallout if a nation was caught backing them would be too problematic and they would be near-uncontrollable and totally untrustworthy allies in any case.
Does that mean it's easy to get rid of them? No.
While ISIS has declared itself as a state, the view of the rest of the world is somewhat muddied (emphasis mine):
Since ISIS declared itself a caliphate on June 19, 201410, the group has received extensive attention in the media, and several attempts have been made to define the goals of ISIS and its role in the world. However, ISIS’ claims to statehood are illegitimate and misguided. While organizations such as the U.S. Bureau of Counterterrorism consider ISIS a terrorist organization11, some have ventured to claim that ISIS is not a terrorist group.
This makes prosecuting a traditional was somewhat difficult. If they aren't a state, then how, or, more specifically, where would you fight them? They have no official territory of their own. At least theoretically, any territory they have would technically be another state's land. That complicates things considerably. Any action taken against them would need the permission of the legitimate state, or else you would risk souring relations with that state as well. That certainly doesn't make it impossible, but it certainly complicates things.
Of course, as others here have correctly pointed out, there's also the fact that most countries have a poor opinion of all out war after what happened in World War 2. Thus, they try to exercise self-restraint and avoid war (at least at that level) at all costs.