Cost of childbirth is approx £1600-1800 per birth on the NHS. Cost of a DNA paternity test is currently £100-200, and would drop dramatically with economies of scale. No significant taxes or cuts would be necessary to fund this, and the value to the men who found out they were mislead by one they loved and trusted would be priceless
The costs of births are irrelevant. This would be an extra cost and one that isn't impacted by the state spending money on other things that aren't DNA tests.
Even if we charitably assume that economies of scale would allow a decent system to work for, say, £75 per child, there are about 700,000 live births in the UK each year. That's £52.5 million before we even get onto the inevitable issues with fuck ups because they will happen when humans are involved and if it got outsourced to the lowest provider which it would. I can see the compensation awards now. The reality is that many of us feel that money could be used much more beneficially elsewhere.
Your use of the terms significant and priceless are value judgements specific to you only. I for one am not willing to spend money that could be more usefully placed elsewhere on something that is already available to individuals and that also carries considerable potential for invasion of privacy and fuck ups.
It would be very simple to do, just make a charge for registering a birth and it would include mandatory testing. No extra taxes needed then.
That sounds like a superb way to price the poor out of registering their children promptly. Even charitably using that £75 figure I mentioned, you're talking about a sum some people just don't have.
Whenever this idea comes up, there are always people proposing it like it's some blasé easy thing, and they've clearly given no real thought to how it would actually work. The fact that anyone thinks it's acceptable to push the costs of their shit idea onto the general population is astonishing, really. If a man wants a DNA test now he can get one. He can do that without obliging me and my family to pay for something we neither want nor need.
But even setting that aside, there's so little insight shown into the reality that for this sort of thing to have any real teeth, the state would end up with access to the DNA of most men in the long run, and that's going to require coercion. It's so very open to abuse. I could name any bloke I wanted as one of a number of potential fathers and I could make him give his DNA away, regardless of whether he wants to or not. There would be nothing to prevent me from doing that every time I have a child, and you cannot sanction this because deterring a woman from naming any potential father means more children won't get the DNA proof some of you seem to think so essential.
When it comes down to it, it's an expense that would have to be paid for from somewhere, it would either be state funding or obligatory universal private funding for something that individual men can already arrange for themselves, it would require the compulsory handing over of DNA of children whose parents don't want it and men who don't want to be involved either, and there's no way of knowing whether the suffering caused by the inevitable mix ups will be any less than the suffering caused by lies now.
Basically, it's a fucking shit idea.