I have some theories about away rotations. I think they are good for 1) Letters of rec. 2) experience at other programs/institutions. 3) opening yourself up to a region from which you are geographically distant. 4) getting an invite at a mid-lower tier institution and moving you up the rank list if you do well. 5) getting an interview at a high tier institution if you're VERY near making the cut for their interviews anyway and you did GREAT on the rotation.
I'll expand on each of these:
1) LOR: If you come from an off-brand institution with a small department and not particularly well known people, this is pretty important if you ask me. Getting a big-wig letter or two, I feel, was very important for my application. People from big places don't need to go elsewhere for letters unless they have reasons they can't get them from home
2) Experience: This is the true best purpose of away rotations, in my opinion. I really learned so much about how things are done differently at other institutions. Coming from just one place (particularly if small) you "don't know what you don't know". I gained a lot of insight into what my career goals were by seeing other things.
3) Geography plays in when you're trying to get interviews. Particularly outside the top tier. I'm from the southern east coast. I don't think I would have gotten the interviews I did on the west coast if I hadn't rotated out there. Top tier places can offer who they want b/c people will travel. Mid tier places aren't going to offer someone with no ostensible reason to be in a distant place unless you give them a reason. Rotating is one way. Reaching out in your personal statement might help.
4) While this is a competitive field, places still want to get their top choices, and good programs still scramble. If you're a strong applicant, expressing interest in a mid-tier place by rotating can provide you a good foothold in an institution. If you do well, they think you want to come (well heck you rotated...), then I think in this scenario it will move you up the list.
5) Based on what I hear on the trail, I don't think rotating buys you an interview to a top place if you're not already qualified. Here's why I think that's true: Besides the discussion here of how easy it is to mess up in a 30 day period, I think it goes deeper. Rad Onc program directors get amazing applications. Many people seem to sparkle on paper. But when you meet them, you realize that most students are "pretty good". It's very hard to impress a resident or attending in a field you're a novice at at this point. So you can work hard, be really prepared, do a great presentation... but in the end how do you make someone think you're so amazing? I haven't figured out a way how, and in all of my rotations with dozens of other students, I'd describe almost all of them as "pretty good". Including myself. I'm super new. I mess things up. I try hard. I'm not stupid. I'm usually fun to be around but I rub some people the wrong way. So unless you're one of those invisible unicorns that can dazzle experts in the field, I don't think your hard work and personality will make up for your non-competitive scores, pubs, activities, etc. Not at top tier places. SO given the fact that you're probably a "pretty good" medical student, imagine a PD looking at a stack of amazing applications. Perhaps yours is one of them. But they know you. So what you might have done by rotating is taken some of the shimmer off of your application. They knew you were "pretty good". But this other application... this person might be amazing! Look at all they've done. Look at their volunteer work. Their academic record. Wow!! In that scenario, I think the mystique of the student they haven't met based on their paper application trumps the equally glittery application of the rotator who was "pretty good".
If you're not on par with their normal interview pool, I don't think rotating gets you a spot unless you totally nailed it at every level.
Whether or not doing a rotation will move you up on the list, I'd say, is also debatable. I bet at mid tier places, it helps. At top tier places, I'm not sure. Historically it seems like 50% of folks match either at home or where they rotated. This seems to point towards rotating helping you match, but I'd also mention that this is likely to self select really heavily. Lots of people rank home/rotation locations highly, and their "pre-match probability" of wanting to go there is also high. So who knows.
For context, I'm a current cycle applicant, and I rotated at a top 5 and top 30 (if you believe doximity) place. I got invites to both. I don't think I shined so brightly that I bought myself interviews, but I think it helped a lot with geography.
Of course this is all speculation... just ideas I've got that could be completely wrong.