The summer interns are more like errand-running type of people. They're not qualified to actually work on patients and whatnot. They might be assistants, depending on the job, but the real interns - the ones who have finished school - are going to be the priority. If they intern for 2 or 3 years, they're probably more likely to get hired on immediately as a healer once they complete their schooling at Hogwarts and won't have to go through the internship program. The people who are already graduated are the ones who will be hired on first, though.