Curious: what do you mean by "dream"? After all, private fire companies actually exist on planet earth. In my dictionary, they qualify as "real".
Suppose there is a fire in a densely packed area. Does the privitized fire company have an obligation to any other property owner not a subscriber?
You appear to be implying that the fire company has a positive obligation in this regard. I believe I can make a solid argument that it does not. However, their practice seems generally to be to do what is necessary to save life, but do nothing extra to save non-subscribers' property. For example, a couple months ago such a case came up. The company answered the call, and suppressed the fire until everyone was out of the building. Then they let it burn.
Consider a fire in one of three interconnected buildings. Company A services building 1&3. The fire in building 1 has spread to 2 and perhaps endangering 3. Can this company use demolitions on building 2 to preserve building 3? Are they serving their clients if they do not? What liability to the owner of building 2?
Very good question. There are answers to it, though. Private property is paramount. Destroying someone else's property is not an option, so demolishing the property-owner's home without consent is not acceptable. However, there are multiple available options:
The fire company might decide that it's cost-effective to put out the fire in the middle structure. For example, the fire company might be paid by the insurance company, and the cost of putting out the non-subscriber's fire might be less than the cost to them if the subscribers' property is extensively damaged.
The fire company might decide it's cheaper to buy the milddle house and demolish it. Under the circumstances, the owner is likely to give them a pretty good deal.
The fire company almost certainly has a non-subscriber price at which they will put out the fire--namely, a full reimbursement for all firefighting costs, plus whatever premium they deem appropriate. They can point this out to the owner of the middle structure.
They can fight the fire as best they can, trying to minimize damage to the covered buildings, but not worrying about the amount of damage to the covered building.
Something else I haven't thought of.
By 'dream' I meant that all fire fighting would be privitized just like they dream that all police and courts and roads would be privitized.
"You appear to be implying that the fire company has a positive obligation in this regard."
Depends upon whether it's a private or a public fire company doesn't it?
"However, there are multiple available options:"
In theory, any of those might work but why prefer such complicated solutions to the very workable solution of public fire companies?