There are, indeed, several such mAb based treatments. From the Mayo Clinic:
The monoclonal antibody drug rituximab (Rituxan) attaches to a specific protein (CD20) found only on B cells, one type of white blood cell. Certain types of lymphomas arise from these same B cells. When rituximab attaches to this protein on the B cells, it makes the cells more visible to the immune system, which can then attack.
Cetuximab (Erbitux), a monoclonal antibody approved to treat colon cancer and head and neck cancers, attaches to receptors on cancer cells that accept a certain growth signal (epidermal growth factor). Blocking this signal from reaching its target on the cancer cells may slow or stop the cancer from growing.
The monoclonal antibody bevacizumab (Avastin) targets a growth signal called vascular endothelial growth factor (VEGF) that cancer cells send out to attract new blood vessels. Bevacizumab intercepts a tumor's VEGF signals and stops them from connecting with their targets.
Ibritumomab (Zevalin), approved for non-Hodgkin's lymphoma, combines a monoclonal antibody with radioactive particles. The ibritumomab monoclonal antibody attaches to receptors on cancerous blood cells and delivers the radiation.
Ado-trastuzumab emtansine (Kadcyla) is one such drug approved to treat HER2-positive breast cancer. Ado-trastuzumab emtansine contains an antibody that attaches to the HER2 receptors on the breast cancer cells. The cancer cells then ingest the antibody, which releases a few molecules of chemotherapy.
It does eliminate side effects, although the treatment is not side effect-free.
Personally, my suspicion with this approach is this: At its heart, cancer is a problem of uncontrolled cell division. Most cells in the body do not divide rapidly, and this slowing down of proliferation is integrated into differentiation into whatever tissue the cells are in. The most obvious cells that divide rapidly are stem cells (themselves carcinogenic!). Furthermore, it seems to be a common theme in cancer that the less differentiated (or more de-differentiated) you are, the more easily you divide, and hence the nastier the cancer you generate.
As such, the worst cancers out there are going to be very undifferentiated, and express few eligible surface markers. What's more, tumors evolve. If you start selecting against cells which express your marker, you will encourage the tumor to simply evolve and stop expressing that marker. Back to the benchside to look for a new marker - meanwhile your patient gets worse and worse.
This is why generalized chemotherapies (or radiotherapy) are so attractive. They attack the rapid division of cancer cells, and the cancer cells cannot evolve to lose this property, because if they did, they would not be cancer cells.