Ironically, if you deny the importance of IQ, it mostly hurts the smart kids from poor families. Because the rich parents will find ways for their kids to realize their full potential -- whether it is a full potential of an average child, or a full potential of a gifted child. It is the gifted child born in a poor family who won't have a private tutor because their parents can't afford it, but also will be denied by the system because "IQ doesn't mean anything".
Smart kids from poor families need even more help than smart kids from rich families, and we deny it to them in the name of fighting inequality. It's no child left behind the minimum requirements of the school system, but many children left miles behind their true potential; especially the poor ones.
But, you know, the offensive thing about IQ is exactly that it demonstrates that different people have different aptitude. So, in practice, I find it difficult to believe that people fighting against the concept of IQ would be willing to provide sufficient opportunities to children with high IQ.
Sadly, many people's instinctive reaction to a gifted child is throwing some obstacles in the child's way, to "prove" that the child "was actually not that smart". (This is even more likely, if the child is a minority, or autistic, or different in some other visible way.) Some of those people are teachers. I know stories...
Like, there is a girl I know who did math olympiads at elementary school. For some reason, this rubbed her math teacher the wrong way, so the teacher started bullying her in the classroom. Two years later, the girl had phobia of math, and was unable to do even school-level math. Then her parents intervened and transferred her to another school, and with some private tutoring (by me; that's how I know the story) she became a straight A student again, and later successfully completed a university that required a lot of math. She never got back to the competition level, though, because the wasted time made a difference.
This story is less rare than you might hope. Quite many gifted kids, unless they also have superior social skills, are bullied either by their peers or by adults. People are bad at tolerating difference; twice so, if the difference suggests that the different person is somehow superior. And the gifted kids with superior social skills aren't winners here either; when they tell you "I was interested in many things, but I was careful never to mention it in front of my classmates", it makes you wonder what they could have achieved if they were allowed to follow their interests freely.
If you measure achievement based on "percent reading at grade level and passing MCAS", then all high-IQ students are, in effect, "left behind". I agree strongly with your 2nd sentence, but disagree strongly with the first and fourth.