For general surg: as tiredmom mentioned, it helps you manage sicker patients post op on the wards. you will be glad for this when you do gyn onc, or if your gyn onc is weak. not all programs require this (ie mine does not)
For breast surg: several reasons. 1, as an ob/gyn you are learning to provide health care to women, and this rotation will get you involved in a very significant issue to women, about which you must be informed. 2. there are breast fellowships open to ob/gyn's, so some of us may do breast surgery 3. the rotation likely will cover a lot of non surgical breast care issues that you will need in your day to day practice
For all the "off service" stuff...if your program meets the RRC requirements without having to leave the confines of your clinic, they do not have to make you go outside at all, or at least very much. In my program we go off service for one month of inpatient IM wards, and one month of ED. In our clinic we manage a ton of primary care, so no need for additional outpatient exposure. Our surgical numbers are high, so we get plenty of OR time and post op work. We have an extremely busy gyn-onc service, which easily covers the critical care/ICU patients. So, it is program dependant.