This is a common proposal. It's laudable in principle, but there are a number of problems with it.
First, the industry has moved on. Recreating the Apollo project would mean regressing to a mode of design, construction, and testing that is no longer practiced and would be prohibitively expensive to resurrect.
While the hard work has been done in the sense that the foundation science still exists and the designs are committed to paper, there is much more to actually executing the design. NASA is currently exploring whether to rebuild the Rocketdyne F-1, and they've had to call a lot of people out of retirement to fill in the many gaps. Four years is about the limit of corporate knowledge in aerospace. To this end, we maintain -- in several aerospace companies -- "trickle" programs where we fund the engineering and manufacturing of certain once-critical things at a trickle pace, just so we don't forget how to do it. We've found over the decades that this is far cheaper than trying to get it going again once it's stopped.
Sadly the Saturn V is no longer street legal. Not only has the industry changed, but so has the law under which it operates. Nowadays rockets that use frangible and pyrotechnic fasteners have to employ capture devices that prevent the shards from becoming hazardous debris. The Saturns didn't have those. That opens to a broader issue of increased safety concerns. In order to fly the Saturn V again, the design would have to be adapted to bring it "up to code," as they say in the building trades.
And that comes down to the bottom line: If we were going to reproduce Apollo today, we really would want to do a better job of it. While we would certainly build upon the experience of the past -- note how much Orion looks like Apollo, and works like it -- we would need to use modern techniques and comply with modern standards. And that would result in a similar, but different product.