I might be wrong but I don't think that larger tech companies get that many more applicants for jobs than smaller companies do. Beyond FAANG I don't think there is really much more "status" around working for a large company vs working for small company. Most people understand that just because the company you work for is large one doesn't mean your job is any more challenging or technically advanced than it as at a small company.

Also a company hiring a mid-level developer (say around 3 years experience) doesn't really have that much of a pool to chose from. Most good developers are already in jobs and pickings are slim, its a buyers market.

Larger companies usually have more brand recognition == more applicants. Many smaller companies are essentially unknown to the public and need to rely much more on talent agencies to bring in applicants.