I think you're imagining that this would be a good way to get a foot in the door, but many internship programs are more competitive than full time programs.
Partly this is because they usually have limited spots.
Another large component is the makeup of the applicant pools. Internship applicants include lots of strong applicants that won't be in the full-time applicant pool because they'll get hired out of internships.
Anecdotally, our coding screen gives intern applicants a median score 13% higher than full-time applicants.