Is it reasonable to have a mastectomy for early-stage breast cancer and not have chemo or radiation?

It Depends. A mastectomy does not guarantee you won't need chemo or radiation. The tumor's "personality" determines that. After a mastectomy, you might need chemo if the tumor is aggressive. Chemo treats your whole body to kill cancer that may have traveled. You might need radiation if you have positive lymph nodes, or if cancer was near the incision site. Ask your oncologist. It's complicated!
Yes. It is reasonable but survival is equivalent with lumpectomy and radiation. A mastectomy would be recommended for inflammatory breast cancer, multiple sites of breast cancer in same breast or for those with a brca mutation. If there are not these things present it often becomes a personable decision whether to have a lumpectomy or mastectomy.
Yes. It is very effective to have mastectomy but not any more effective. It's the choice of the patient which option they prefer and best suits them. However even in early stages many times chemotherapy or hormone therapy may still be recommended to improve the odds or survival.
Why no chem/XRT? The current practice is to treat all non-invasive (intraductal) cancers, but there are methods to forecast who may not benefit and thus avoid radiotherapy. Chemo/radio used for invasive cancers can be avoded for very small tumors, with no signal of invasiveness or nodes. When in doubt, seek more than one opinion in each modality.