The bigger problem there is that we don't have the people any more.
The Rocketdyne F1 was the pinnacle of hand-crafted engineering, with each engine being slightly different and the people having to account for those differences during assembly. It has a whole bunch of complicated welds which require a lot of tweaking, adjusting, and literally days of welding work? Neil's got to go to the moon, so you better get to it!
Those highly-skilled highly-specialized engineers don't exist any more, and for a good reason: with CNC and robots we can achieve far superior results for a fraction of the cost. It just requires the designers to make it automation-friendly from the start. Those skilled people retired (and by now died) without a replacement, because the job had become obsolete.
So no, we literally cannot build a new Rocketdyne F1. We can design and build a better F1-like engine, though!