I just looked at matriculation exams from Finland. They have both basic and advanced level exams. Most US high school seniors could not pass the basic exam. If each US state were to create its own math matriculation exam, with basic and advanced options, the level of math among college freshmen would increase tremendously. Why there is no attempt to emulate Finland, whose education is considered the best in the world?
Finland is a small country with a centralized political system and a university system that is essentially public and free, and highly centralized on a couple of big schools. The US is a big country with a federal system of government and a higher education system that is a mix of public and private, spread across an entire continent. In the US, the federal government has essentially no role in education -- it doesn't fund it and only regulates it in certain very limited ways.
So the first barrier in your plan is that it can't be instituted politically. The federal government is not going to expropriate the University of Chicago from its private owners, take over Cal State LA from the California state government, etc. Without that kind of centralized control, you can't institute national standards for college admissions.
The second barrier to your plan is that the electorate in the US doesn't want it. The voters have decided that they want higher education in the US to be very broadly available. In Finland, it looks like about 3% of the population is enrolled in higher education at any given time. In California (whose population is 7 times greater than that of Finland), the figure is about 6%, of which about half is community college students. (Counts of community college students are somewhat meaningless, since many CC students have only tenuous ongoing ties with the schools where they are theoretically students.) Community colleges have nonselective admissions. By your plan, they would close up shop, since the four-year schools already have enough capacity for the number of students who quality under any kind of selective admissions standards.
You seem to imagine that in Finland, the examination requirement has made everyone graduate from high school with a high level of academic preparation for college. That doesn't seem to be the case, since their total enrollment in schools with selective admissions is about the same as ours, at 3% of the total population.
Standardized testing is great. It's one of the few things that prevents the total dumbing down of education to some kind of horribly low level dictated by popular demand. It's also great because it's one of the strongest anti-racist and anti-classist institutions in our society. It's a barrier to the kind of racism and classism that says that it's OK for a high school with brown or working class students to provide inferior educational opportunities and pretend that those opportunities are not inferior. But a standardized test is sort of like a COVID test. It doesn't cure the problem, it just makes it harder for policy makers to hide their heads in the sand and pretend that nothing is wrong.