I don't think that is accurate...
The output of id Software after Romero left (post Quake 1) was a clear step down. The technology was fantastic but the games were boring and uninspired, at best "good" but never "great". It took a full 20 years for them to make something interesting again (Doom in 2016).
After Romero left, id Software's biggest success was really as a technology licensing house, but not as a games developer. Powering games like Half Life, Medal of Honor, Call of Duty, ...
Meanwhile Romero's new company (Ion Storm) eventually failed, but at least the creative freedom there led to some interesting games, like Deus Ex and Anachronox. And even Daikatana is a more interesting game than something like Quake 2 or Quake III.