Joy,
Your assumption is right.
Under certain conditions cryoablation can treat cancer effectively & with much reduced pain, reduced scarring, no anesthesia,no or short hospital stay.
In the case of breast cancer, cryoablation is applicable to single tumors less than 1.5cm & is no more invasive & difficult than a core needle biopsy both of which can be done in a doctor's office:
http://www.touchbriefings.com/pdf/1438/Kaufman.pdf.
Cryoablation – The Next Advance in Breast Cancer Care?
An other recent example of the use of cryoablation:
http://patient.cancerconsultants.com/news.aspx?id=38656
Cryoblation May Help Preserve Voice in Glottic Cancer
For men with either BHP or prostate cancer cryoablation is also possible:
Endocare's prostate cancer study reveals 100 survival after 8 years following cryoablation
But the most common application of cryosurgery remains outside the field of cancer : the cataract operation which runs in the millions every year.
And here the aim is not kill the crystalin but to solidify its normally soft consistancy so that it can be brocken up into small particles (under ultrasound vibration) easily extracted from the eye through a minimal size hole.