I've applied for a PGCE this year, so I've been reading a lot about what people have been rejected for in previous years, and the most common reason appears to be a lack of subject knowledge, perhaps combined with other weaknesses at interview. People who didn't get interviews seemed to lack essential qualifications or not have any classroom experience (but these seem pretty rare anyway).
As you can apply to 3 courses initially via UCAS, institutions must over offer already. Also, if an applicant doesn't get into their three initial choices, they can apply through "apply 2" until they get an offer or there are no more spaces. This suggests to me that anyone with the capability to teach will probably find a place.
If you assume the same candidates probably get rejected multiple times, then 50,000 rejected applications is probably less than 20,000 individuals. I guess more of these individuals would be applying for popular subjects like PE and history.
Offers are conditional on passing a DBS and health checks as well as passing skills tests if you haven't already. If these candidates are included in the numbers listed, arguably they aren't people who you'd want teaching your children.
As a solution, maybe recruitment could be more targeted. I think schemes to send STEM undergrads into schools as teaching assistants/volunteers could help them see that not every school is a horror story in terms of behaviour, and might encourage them into teaching.