Good questions.
I believe it is worth studying and debating the definition of intelligence. I believe modern IQ tests do a reasonable job of crystallizing a value which is both meaningful and useful. In general, the goal is to quantify an individual's mental potential, which might be understood as their processor speed, amount of RAM in their brain, pre-programmed learning algorithm, and so forth. As with any concept in social sciences it's difficult to define it perfectly, but I believe it's worth the effort.
As for why we should care?
1. Western societies spend incredible amounts of resources on programs to equalize opportunity for people. Large fractions of this money in most western nations are allocated based on what I view to be a misunderstanding of what enables a person to prosper financially or otherwise. Examples include universal preschool and the like. Accepting the reality of IQ would assist in eliminating ineffective programs and allocating capital more effectively.
2. The quasi-religious doctrine of universal racism is an existential risk to modern liberal democracy, and it is built fundamentally on the false premise that IQ is environmental or doesn't exist. Eliminating that premise would allow consideration of other explanations for differential outcomes between groups that don't rely on accusations of hatred and bigotry.
3. Major research institutions across America and abroad, as well as large corporations, risk decreasing the rate of technological and economic progress by implementing programs built on a quasi-religious premise that people are treated vastly unequally for reasons having nothing to do with their capability. Accepting IQ as a valid science and explanation would not only de-taboo important potential areas of research, it would eliminate costly and wasteful efforts which will never bear fruit, as they seek to address problems which don't even exist.
4. An incorrect understanding of the causes behind achievement gaps provides onramps to corrupt political participants who take advantage of the basic logical fallacy that "false statements can imply anything" to redirect funding and attention away from pressing issues. Concretely, this results in death and violence resulting from failure to properly apply the law and failure to differentiate between what is true and what is false. "Without vision, a people perish."
5. Acceptance of IQ enables creation of tiered magnet schools, trade schools and other opportunities which benefit all of society, particularly those who are at the bottom of the economic ladder but who test high. Instead, at least in America, the trend is toward the elimination of all magnet programs because they are "racist." The harms here are obvious, and they all stem from an unwillingness to even consider that IQ exists and might be genetic.
6. Refusal to discuss IQ leads to it being something that is whispered about behind closed doors, but cannot be discussed openly. This directly harms those who are often (and often wrongly) associated with groups that might be thought to have lower IQs. Bringing the reality of IQ into the open enables a real conversation about it, and it allows confronting racists on much more solid ground, since the debate is no longer undergirded with taboos and untruths.
7. Acceptance of IQ allows targeting social programs toward the truly needy, accounting for the reality that in modern human life, IQ is the variable that best correlates with material success. This would eliminate injustices like affirmative action programs going to wealthy immigrants from other nations instead of those truly in need. It levels the playing field and could serve as a basis for rational policy such as targeted universal basic income.
8. AI research will ultimately force us to accept IQ as largely genetic. Accepting IQ now will avoid some sort of schism in the coming decades over this question, and allow a more rational discourse over AI's role in our lives and how to best harness it and avoid its risks.
Is that sufficient?