Why do these kosher foods need a hechsher?
This question is not easily provided but mainly they require a hecksher because of the process they undergo, and the chemeicals that process is making them go thru. {Some} chemicals have non-kosher animal bi-products and make potentialy kosher food products non-kosher which is obviously a reason to disqualify them as kosher, because the chemicals that have been processed alongside the food products means that they would be eaten by the jew and would constitute eating the forbidden foods and that will result in a breech in halacha and the Torah states we are to becareful in our observance towards his mitzvot. Edit—–To know what chemicals may or may not be used you would need to read the ingredients and determine [by halacha] wether you can use this or that. For instance your very first product [tomatoes] you mentioned does not require a hechsher if they are plucked from it’s branch but if processed and placed in cans then it would require a hechsher because of the process it underwen
