Yes. Under the current system it IS a 'benefit'.
To put it absolutely bluntly, awful as it sounds, the NHS and Education exists because society as a whole needs a healthy workforce with a reasonable level of education. It benefits society as a whole to have this. Once the country has ensured those needs are met, it could be considered it has given people every tool they need to manage everything else by themselves.
Some people, however, can't manage these things for themselves, or in some cases they just don't. The government cannot afford to pay for everything for everybody all the time, but it's not terribly humane to let people die of starvation and hypothermia because they cannot house or feed themselves for whatever reason, even if some people feel that some don't have a good reason for not providing for themselves, despite the tools given. Those people get benefits paid for by people who may never need them. Because there isn't a lot of point asking people with no money for money. It's how we care for our most vulnerable. But we can't afford to do it for everyone. We can only do it for those who need it, and they need it because they have no money. It doesn't benefit you or I, though, in quite the same way a fit and educated workforce does. That's why it's a benefit paid according to individual need, rather than a blanket payment.
At the other end of the scale, the end we are talking about, the same applies. It doesn't benefit society as a whole to provide elderly care for everyone, regardless of financial status. But to leave those who have no money to fend for themselves would be an awful thing to do. So, like the benefits given for food, housing etc, we pay for those who have nothing, or not enough, using the money from the people who do.
I think the misunderstanding lies in imagining the NHS and State Education exist purely for our benefit as individuals. They don't. They exist to help maximise the number of people who can work and can pay taxes, which aren't all for benefits, but which also pay for our roads, our civic structures like bridges, etc, and the maintenance thereof.
If we want a society where everybody gets exactly what they think they pay for, regardless of what independent means they have, taxes would have to be about 80% of income for everybody working. Of course, we could do that. We could provide everything for everybody - food, shelter, health, education, elder care - and pay for that through taxation. But in order to do that, we need the majority not just working, but being paid more or less the same, otherwise you will still have people who will end up paying more than others. That system looks rather familiar to me. Sure I have seen it somewhere before and I don't think it ended too well...
The reality is that, fundamentally, I agree that we ought to change the system. But trying to dodge the system we have already simply takes the funding away to the point where the services disappear for ever.