A 4070 is absolutely enough for 4k / 60 FPS, unless you're talking Cyberpunk with its new pathtracing mode. With the abundance of modern upscaling methods like DLSS2/3, FSR2, Xess, games will be rendered at lower resolutions internally anyway. I'm running 4k with a 6700XT, which is perfectly ok if you accept 'high' instead of 'ultra' quality settings.
The 4070 isn't built for longevity though. The 12 GB VRAM are just enough for today's games at high resolutions, in a few years it will have issues related to vram size, like its predecessors do now (the 8gb 3070 and also 10gb 3080).
There's already games which would be severely limited by the 3800X though, Jedi Survivor being the most recent and worst example. CPU limits below 60 FPS are a reality for most CPUs out there with dips in the region of 20-30.