This is a common understanding in power industry which however may not be true. Normally convergent solution contains Bias if bad measurements and/or system modeling errors are not all effectively detected and removed. Therefore, some weird problems occur from the convergent solution, such as negative loads at some buses, big mismatch at some buses, branches generating real power, etc. The biased solution will have negative impacts on the performance of other functions including contingency analysis, LMP calculation, security assessment, etc.
Let us take the best convergence rate 99.8% as an example. Normally state estimator runs every 5 minutes (it is even shorter for some companies), which means state estimator needs to run 288 times every day. 99.8% implies that there is at least one-time divergence every day in average. One-time divergence per day is not a big deal unless the system is in alert state or is under extreme tense, like what happened in 2003 Northeast blackout.
In 2011 it was reported in "The Future of the Electric Grid: An Interdisciplinary MIT Study" that “the algorithm (of state estimator) is not perfect, and state estimators have trouble estimating a system state during unusual or emergency conditions – unfortunately, when they are most needed”.