What if it is the other way around? Early introduction of peanut and fish seems to be better than avoidance.

UNLABELLED: For many years, the advice to prevent food allergy was to postpone the introduction of allergens like egg, fish and peanut. However, elimination of food allergens during pregnancy and infancy failed to prevent food allergy. Instead, several studies indicate that early introduction of food like fish and peanuts may be beneficial. The most compelling illustration of this has been presented for peanuts. The prevalence of peanut allergy is lower in children in Israel than in the UK, despite introduction of peanut during infancy in Israel. Other studies have reported that early introduction of fish reduced the risk of allergic sensitization and allergic diseases like eczema.
CONCLUSION: Early introduction rather than avoidance may be a better strategy for the prevention of food allergy. The mechanism may be that early introduction of food allergens during infancy might induce tolerance, thereby preventing the development of allergy.