It is only appropriate if you cannot conceive government actions that have nothing to do with force :)
Would you call policing a 'war on crime'? The enforcement of contracts a 'war on fraud'? The collection of taxes a 'war on free-riding'?
The deficiency of 'war' as the correct metaphor here is that war implies much more than simply 'force'; war has a particularly structure, in part:
1. It is a conflict between distinct groups
2. It is the exception and can be distinguished against 'peace'
3. Victory, or defeat, is possible (in ancient times, where warfare was common and vicious, the literal elimination of entire polities was very common)
None of these things are true of the 'war on poverty' or 'war on cancer', for example.
A war does indeed have a structure, but I'd disagree with your list a bit. Your point 1 is correct, but "groups" is a fungible category and we've certainly seen wars that included the attempted destruction of both groups of people and concepts (history, religion, ideology, etc). 2. Unfortunately history argues that peace is the exception rather than war. There are plenty of wars occurring right now in which we have no participation, nevermind those that we do. 3. Plenty of wars ended with no victory or defeat, and it's certainly arguable that in some cases neither was realistically possible.
I specifically left out the War on Cancer because a good portion of it was under the aegis of private parties, not that it much mattered when it came to the failure of results. They originators believed that Cancer was a single entity that one muster all efforts against... they were wrong.
That the wars waged were wrong-headed in both conception and means is pretty obvious, the means simply ensured that the consequences would be much closer to actual war.
This isn't a metaphysical question, this is literally how modern governments are able to exist and operate at scale and how your dollar bills or local equivalent have any value at all.
The biggest chunk of government use or threat of violence is in property rights enforcement. Anything on top of that is mostly peanuts.
For example, if a local government raises property taxes by 5 percentage points in order to get the funds for better schools, there's likely no additional use of force at all. So it's absolutely possible to raise living standards without use of force for all practical purpose.
A reasonable libertarian who worries about use of force (but I'm aware that such people are so rare they may as well not exist) should be in favour of such a policy, because it increases the ratio of "quality of life per use of force".
It is not the linearity of the USE of force but the threat that matters. I support any number of government actions knowing full well that those actions very well can result in the use of force. I understand and accept those consequences as part of my moral duties rather than try and hide from them.
A diminution of force is not the absence of force and you simply can't have a government act without the consequence of enforcing its actions. This isn't "cooperative" since that requires voluntary consent of all parties. I may support any number of government actions but I do not hide behind euphemisms to convince myself that those actions carry with them the very real potential and actual consequence of force.
Gardening is often proposed as an alternative metaphor to the more common metaphors of war and sports.