Problem is not the creation engine, the problem is that both Skyrim and FO:NV tried to do to push the hardware to far.
One obvious effect is framerate dropping, an secondary is instability, this is well know among pc gamers if you run an game close to minimum system requirements it will be way more unstable than on an pc who runs it smoothly.
This is not an creation engine issue, GTA 5 has the same issues on previously generation. DA:I does not release dlc on previous generation.
Now Fallout 4 should not have much issues, full hd on One is not common among graphically intensive games for PS4/One/PC.
Now all engines are under constant development, creation engine has been developed since the start of Morrowind for open world games with lots of details.
Zenimax owns multiple engines who Bethesda could have used, they did not want to use them as they was not optimized for fallout 4 as they wanted it to be.
https://en.wikipedia.org/wiki/List_of_first-person_shooter_engines
Note that open world is the new buzz world in the game development world. Skyrim and GTA caused this, now gta series focus on far larger worlds because cars are central in the game, this reduces details.
No they could not used Id-tech engine, its not designed for an game like Fallout or TES, technical issues in that everything is in one giant texture map.