Your second statement is incorrect.
Having a racial bias would mean that IQ tests are incorrect (having significantly different errors) for certain samples/groups. But no one is saying that.
Imagine a test to measure the resistance of various materials. Is the test biased because it shows that concrete is stronger than rotten wood? No, it just measures the resistance of different materials. If the measurement error (not the measurement itself) was significantly different for different materials then yes you could say the test is biased.
You are just saying that SES affects intelligence, which is most likely true and immediately prompts the question of what affects SES.
A large percentage of the population seems to believe that IQ and similar cognitive ability tests are something like a credit score, having no purpose but to direct society to the high scorers so that they can be showered with opportunity, while denying the same to low scorers. And it's true that tests like the SAT can have a big impact on the opportunities we get in life. But they can also be used in a more win-win way, to match people to opportunities they're ready for. And for that, you need an honest assessment of where the person is actually at, separate from how they got there.
A poor kid may score worse than they would have scored if they weren't poor, but if we want to know whether they're ready for MIT or a course above their grade level, it might do them a disservice to confound our perceptions of their actual current level with our personal indignation over socioeconomic inequalities and our hopes in the potential they'd realize if those inequalities were eliminated.
Imagine a test to measure the resistance of various materials. Is the test biased because it shows that concrete is stronger than rotten wood? No, it just measures the resistance of different materials. If the measurement error (not the measurement itself) was significantly different for different materials then yes you could say the test is biased.
You are just saying that SES affects intelligence, which is most likely true and immediately prompts the question of what affects SES.