The not guilty verdict was correct based on the case presented. The system, as it is, worked properly.
Oh and by the by, lying to the police should not be a crime (defrauding the police is one thing, but simple lying... 5th amendment issue).
The prosecution failed to even make any serious attempt to conclusively prove that the primary charged crime was even committed (other than lying, obstruction, and evidence tampering of course; but those were not the primary charges).
They failed in this, because they had no real evidence of it. Their only case was to basically say "isn't this awful. It has to be her fault. No-one would do this unless they were a horrible awful person and she should pay for that".
Frankly, the charges never should have even been brought. They knew there was no way they could prove them before they ever filed. They filed based on the political pressure form the aftermath of the "missing child search"; and they were counting on the jury hating the defendant so much they ignored the lack of evidence.
That didn't happen.
Frankly, that is a common prosecution strategy; particularly with black defendants in majority white areas, drug users, accused child molestors, and women they can paint as "sluts" or "bitches". Push the "mommy" and "morality" buttons on the jury and give them enough horrible crap to process that they just want to punish somebody.
But that isn't good for justice. It's a strategy for winning, not for finding the truth, or protecting the innocent. It's a strategy that has put a lot of innocent people in prison.
And it didn't work this time.
Did she kill her child... I don't know. It seems likely, but not certain. There are certainly credible alternative theories; though the most likely is that she did. If she did, did she do it intentionally? I don't know... I can't even say it seems likely. It's possible, but entirely uncertain.
That, by definition, is a not guilty verdict on the charges presented.
The system worked.