No, their algorithms and heuristics are not especially good.
The reason for their quasi-monopoly is the one stated by another poster, that the 3 big EDA companies have privileged relationships with TSMC and the other major foundries so they have access to information that is not available to anyone who would want to develop alternative EDA tools for state-of-the-art CMOS processes and not for ancient processes down to "28-nm" (i.e. at the level reached in 2011, 15 years ago).
The reason for their quasi-monopoly is the one stated by another poster, that the 3 big EDA companies have privileged relationships with TSMC and the other major foundries so they have access to information that is not available to anyone who would want to develop alternative EDA tools for state-of-the-art CMOS processes and not for ancient processes down to "28-nm" (i.e. at the level reached in 2011, 15 years ago).