I'll limit this to alcoholic mouthwash and capsaicin, the chief spiciness compound in chilis.
I am too much of a wuss to do spicy foods. However, when I read the "burning off tastebuds" in title of your question, what came to mind was the real reason why I use alcoholic mouthwash -- for that sensation that comes around after 30 seconds of swishing it around in your mouth. I wouldn't quite call it burning off your tastebuds, but it does feel like I've burned something.
In which case the use of alcoholic mouthwash is a risk factor for oral cancer. This interesting paper looked a genetic polymorphisms involved in alcohol metabolism as well:
Oral health, dental care and mouthwash associated with upper aerodigestive tract cancer risk in Europe: The ARCAGE study
Objective We aimed to assess the association of oral health (OH), dental care (DC) and mouthwash with upper-aerodigestive tract (UADT) cancer risk, and to examine the extent that enzymes involved in the metabolism of alcohol modify the effect of mouthwash.
Materials and methods The study included 1963 patients with incident cancer of the oral cavity, oropharynx, hypopharynx, larynx or esophagus and 1993 controls. Subjects were interviewed about their oral health and dental care behaviors (which were converted to scores of OH and DC respectively), as well as smoking, alcohol drinking, diet, occupations, medical conditions and socio-economic status. Blood samples were taken for genetic analyses. Mouthwash use was analyzed in relation to the presence of polymorphisms of alcohol-metabolizing genes known to be associated with UADT. Adjusted odds ratios (ORs) and 95%-confidence intervals [CI] were estimated with multiple logistic regression models adjusting for multiple confounders.
Results Fully adjusted ORs of low versus high scores of DC and OH were 2.36[CI = 1.51–3.67] and 2.22[CI = 1.45–3.41], respectively, for all UADT sites combined. The OR for frequent use of mouthwash use (3 or more times/day) was 3.23[CI = 1.68–6.19]. The OR for the rare variant ADH7 (coding for fast ethanol metabolism) was lower in mouthwash-users (OR = 0.53[CI = 0.35–0.81]) as compared to never-users (OR = 0.97[CI = 0.73–1.29]) indicating effect modification (pheterogeneity = 0.065) while no relevant differences were observed between users and non-users for the variant alleles of ADH1B, ADH1C or ALDH2.
Conclusions Poor OH and DC seem to be independent risk factors for UADT because corresponding risk estimates remain substantially elevated after detailed adjustment for multiple confounders. Whether mouthwash use may entail some risk through the alcohol content in most formulations on the market remains to be fully clarified.
There's quite a bit of research regarding anti-tumour properties with respect to other forms of cancer e.g. pancreatic cancer, but very little regarding possible risk in oral cancer.
There is an excerpt from A screening model for oral cancer using risk scores: development and validation that does state the following:
People who rated the spiciness of their diet as
six or more had higher odds (OR = 2.15) for devel-
oping oral cancer than those rating the spiciness as
ﬁve or less. This is a subjective measure, but it is an
easier method to collect information on the spici-
ness of food at a population level and in a hospital
setting. In India and other South Asian countries,
red chilli powder or red/green chillies are added
to increase the spiciness of food. These ﬁndings
support the results of other studies conducted in
India that showed red chillies in diet increases the
risk by two-three times for UADT cancers includ-
ing oral cancer (31). Similarly, a higher risk has
been observed for gall bladder (32), liver and gas-
tric cancers (33, 34) in other countries. Although
the association of spicy food with oral cancer could
be due to the carcinogenicity of capsaicin found in
chillies (35), it could be a marker for some underly-
ing dietary aspect in this population.
However, caution should be exercised when using some score on a questionnaire and attempting to correlate it with health outcomes. There is one study cited above that reports the following:
Role of diet in upper aerodigestive tract cancers
A case‐control interview study for assessing the role of dietary factors in selected cancers was undertaken in a hospital. Male patients from one community, with cancers of the oral cavity (n = 278), pharynx (n = 225), esophagus (n = 236), and larynx (n = 80) formed the case group. Patients diagnosedas not having cancer (n = 215) formed one control group, and a comparable sample of individuals from the general population (n = 177) formed another control group. All risks were adjusted for subjects’ ages and habits of chewing and/or smoking tobacco, which are the two most important risk factors for cancers at these sites.
A protective effect was observed with the intake of vegetables (twofold risk in nondaily vs. daily consumers) and fish (two‐ to threefold risk in those who did not eat at least once a week vs. those who did), and to a certain extent with pulses and buttermilk, in comparison with either one or both control groups. Intake of vegetables and fish were also observed to be risk modifiers for those who chewed and/or smoked tobacco. Lower levels of fat consumption was associated with elevated risk levels.
The use of red chili powder emerged as a risk factor for all sites (two‐ to threefold risk with a dose‐response relationship) compared with population controls. Tea drinking was also observed to be a risk factor for esophageal cancers, and to a lesser extent, for pharyngeal cancers.
Unfortunately, it was published in 1986 and there doesn't seem to be any more literature on the topic.
But we might presume, sure, it's biologically plausible and there is some evidence that capsaicin increases the risk of oral cancer, while possibly reducing the risk of other cancers.