About to be an M4 in a week, happy to answer any questions you may have here or in DMs. Drexel does have home residency programs, but not a home hospital. We have a lot of affiliations with multiple hospitals across the country (mainly in PA and DE, some in CA, NC, NJ) that would be considered a home residency program that has preference. A lot of things aren't perfect with moving and having different sites, but there's no real compromise to your education and there aren't any real disadvantages that being a school that sends students away from the medical school location brings.
I can only speak to what I've experienced with getting away rotations for fourth year and what I've seen people match into in the graduating class this year, but generally Drexel students don't find any trouble matching to programs they're interested in going to as long as you do your part in getting good scores/putting together a good CV. Drexel is still a solid MD school with a long history that lends itself to a reputation, so it opens a lot more doors than you'd think despite looking at the "ranking". People match into top tier academic institutions while also being okay with matching into community small profile institutions because Drexel attracts students who have a wide, incredibly diverse variety of goals for their career.