I agree it's the catcher's own fault for putting themselves in a precarious position where they ultimately needed to disappear. However, I'm curious what you mean by her being in an illegal position from the start - please clarify.
What I mean here is: When the runner first slid into the catcher, the catcher was not in possession of the ball. That act, which inarguably led to the runner being impeded at least to some extent, was obstruction. At that time, the catcher's position was illegal. What resulted after that is not particularly relevant, since the runner had already gained protection under the obstruction rule. The only issue that it could affect is just how badly the runner was impeded and whether the runner would be returned to 3rd or awarded home. It's clear here (as in almost any close play at the plate) that the runner would have been awarded home.
Note: My term "illegal position" pertains solely to when the defender actually commits obstruction. At that point, the position is illegal and the runner is protected by implementation of the obstruction rule.