If there's an awesome job available out there, with way above average pay, benefits, great opportunities for advancement, good work/life balance, etc., you'll fill it with a top talent. You're not going to need a recruiter. Word will get around even to people who are not actively looking, trust me. Similarly, if you have an "average pay for an average worker" kind of job, you'll find that average worker.
When you have a ho-hum average job but you want top talent, then you're going to need that recruiter because the job needs to be actively sold.
I invite anyone who works at a company that pays 3X average salaries or is well known for being an unbelievably great place to work to reply and tell me they have trouble hiring.
They could definitely fill their need for new software engineers naturally, but presumably have data that the quality of candidates they get by bothering a substantial fraction of the world's software engineers on ~a yearly basis gets them better applicants and engineers.
Why do you think so? Just because you receive X resumes doesn't mean they're all qualified to work there.
Above average people are usually treated well in theirs jobs. If you want to hire them you need to actively approach and lure into applying. Even then, they will not bother to refresh algorithms questions for whiter-boarding.
Below average people are looking for jobs because they are on PIP or they have toxic relationship with management or they will never get promoted in current role and need to change jobs.
If the quality that companies were getting from regular applications was better than the quality they get from their recruiters why would companies pay to have recruiters?