The calculus issue is if the school you attend wants to have transcendental functions early or later. I feel that having them in calc 2 is better, because you introduce them one at a time as possible forms your integral can take after a proper u-substitution. Also in case yo wanted to know yes, calc 2 is made to be really hard to weed out people who don't have the drive to get into STEM.

Also a lot of math books like to group things into different areas of study. So polynomials and factoring will be before graphing, but I will be teaching graphing first because I want you to get comfortable with parabolas first, and i won't do that before systems of equations which is really linear algebra.

This is mainly done though because it's how Euclid did it. His book(s) Elements was THE math textbook for about 2000 years. For example if you are reading it and want to do only geometry, you look at books 1 - 4. Then 6. Then you skip to 11, 12 and 13 for 3 dimensional solids.