I think you’re straying into difficult territory depending on what tier means to you
There are plenty of people who don’t have much demonstrated talent coming out of high school (maybe there is only one subject they are good at or HS just bored them to tears) and get to college and really turn on
College offers WAY more topics to study than HS
For the most part brilliant scientists or doctors are going to show great aptitude in high school. Innovators? Maybe not. There are innovators in fields that don't do well academically - and often don't even need college.
Further, the U.S. does a good job - certainly better than Denmark - in getting our students a university education. So I am not sure why the focus is on lack of access due to costs as it is the burden of costs itself.