Hello Noah,
First off ATP will not accept any students right out of High School. ATP requires all students to have either their Private Pilot License, a 2yr degree or comparable work experience which means working a full-time job for at least 2yrs. Second while you can get hired at a Regional with no degree, you would as you say “get shot down” when you try to get to a Major (particularly Delta and American). The good news is while the Majors require a degree they are less concerned where you get it so it need not be expensive. A very common route is to go to your local community college and get a 2yr degree. Get trained at ATP and get hired at a Regional within 2yrs after that. THEN work on your BA degree online with significantly reduced credits from you 2yr and pilot licenses and ratings while flying for a Regional. You’re 100% correct it is very possible and you can make it work.
Adam