Could long-term retinoid use prevent skin cancers by repairing sun damage?

Yes, with consistent use over a period of time, topical retinoids can reduce the risk of pre-cancerous skin lesions and skin cancers in the areas where the topical retinoid is applied (specifically squamous cell carcinoma). This is because one of the mechanisms of topical retinoids is to increase turnover of the top layer of skin cells. However, there isn’t evidence that topical retinoid use reduces the risk for melanoma skin cancer, which is the most deadly kind of skin cancer. 

However,  one’s risk for skin cancer is multifactorial, and related to genetics, history of sun exposure, prior history of skin cancer, level of immunosuppression, and other factors. You should also note that prescription retinoids do not have FDA approval for use for treatment of pre-cancerous lesions (actinic keratoses) that already exist. There are far more effective topical treatments than topical retinoids for pre-cancerous skin lesions and skin cancerous prevention.