Most companies want degrees OR equivalent work experience.
Most, maybe. But there are a substantial number that do demand a degree, and the non-degreed will always have at least a small handicap, because given two otherwise equivalent candidates, the one with the degree is likely to get the job, and after 10 years or so the extra four years of experience aren't going to mean as much as the formal education.
In addition, if at some point in your career you want to move into another career track the degree may well become even more important -- though the choice of major may become much less important.