Tooth enamel has no living cells and so, unlike bone, cannot repair itself or become cancerous. However, the tooth does have living cells in the dental pulp, so perhaps they may be susceptible to transformation and uncontrolled growth. Clearly the easy answer would be to consult Pubmed. An even easier solution is finding the one paper that already did that for you, in this case a paper in The Lancet Oncology entitled Teeth: malignant neoplasms in the dental pulp? From the abstract:
[U]sing the search phrase “dental pulp” combined with “sarcoma”, “carcinoma”, or “neoplasms” in PubMed when using the MeSH search mode yielded no reports on primary malignant neoplasms. However, a hand search yields clinical reports on pulpal tumours that were published over a century ago.OK, so tooth tumours do happen - or did over a century ago. Why aren't there any today? Water fluoridation? The authors offer some thoughts about that:
Because of the restricted space in a tooth, tumour expansion will probably lead to the formation of irritation dentine by secondary odontoblasts and, subsequently, to a haemorrhage infarct of the pulp. One hypothesis states that a purported neoplasm of the dental pulp leads to a chronic appositive pulpitis and–sooner or later–will be treated likewise by root-canal treatment or extraction.So dental cancers may be happening with some frequency but manifesting and being treated as other conditions. Or maybe the dentists really know what's going on and would rather pocket the treatment fees themselves rather than referring patients for radiation and chemo. They are, after all, in the pocket of Big Floss.