There was plans in the 50s/60s to have a fleet of nuclear aircraft staying airborne for 2 months. That job ended up being taken by submarines, some staying in mission for 6 months. So the logistic of keeping people and a few ICBM in a metal tube for months is pretty much sorted out. With the hypersonic craze, the money is back to fund scramjets tech too. Nuclear planes are a terrible idea, don't get me wrong, but it's not impossible to build them, it has never been. The problem is radioactive exhaust for the direct cycles ones (the easy one) or reliability for the indirect cycle (the "good" ones).
I am pretty sure material science went a long way. No need to put a foot of lead behind the reactor. The space race provided quite a bit of funding toward lightweight protection. It was too late for those plane project as they were already ramping down in the mid 60's.
Neither that or the plane powerplant are unsolavle problem, it's more of a "why would we invest this much to solve something this silly". Apparently the russians are trying to resurrect their SLAM clone and tested one. How much of this is a realistic military project versus propaganda isn't super clear to me. It's up there along with the manned military space stations in the scale of pointless deterrent PR.
