"How come (should be: why are) police, fire services, welfare (the amount you have), border services (are) all constitutional?"
The answer is these are neither commanded nor prohibited by the U.S. Constitution. Cash money welfare is not and probably cannot be a federal program, there is no constitutional provision for it. The British don't really have a system of autonomous states -- Wales, Scotland and so forth are vaguely similar in that regard. But crime and welfare are state issues; each state has its own criminal code.
The US Federal Government has a long list of things it is not supposed to do and a short list of things it is permitted to do. Everything else is left to the states or to the people (10th Amendment and the foundation of the modern American "Tea Parties").
Anything not prohibited is therefore also not unconstitutional.
Involuntary servitude is prohibited. Mandatory purchase of life insurance is effectively involuntary servitude of the amount of labor it takes for you to earn the money to purchase the mandatory life insurance. in the past such schemes were known by "poll tax" and is dangerously close to mandatory union dues to join a mandatory union to obtain employment in a "closed shop" state. This is the Dark Side of socialism -- socialism and liberty CANNOT co-exist except in the extremely rare instance of people actually choosing a cooperative lifestyle (Iceland is or was a pretty good example 20 years ago).
"There's probably hundreds of nationalised services around, that everyone is just used to."
Yes indeed, but all are fairly recent developments. As recently as 1925, the town where I am now living had THREE distinct electrical distribution companies -- each with its own power distribution wires and poles.
Curiously enough, a British-style National Health System would be constitutional. Not particularly wise, but at least Constitutional and the British continue to provide excellent examples of its good and bad (allowing a man to die of thirst in a HOSPITAL!) sides.
To use a historical example, the United States is believed to have come into existence more or less as a consequence of the Stamp Act by which the King of England imposed a tax on tea. Today that seems pretty ordinary but it ruffled some serious feathers.
It appears that the King should have taken a page from the U.S. Democratic party and required American colonists to BUY TEA, and of course, pay the tax. Alternatively, you could pay the penalty -- the price of the tea, and not actually take possession of the tea. A poll tax in other words. You will pay $5,000 per year because you exist.