The message 'Requested product doesn't exist' is triggered whenever Magento 2 tries to load a product which does not have a SKU.
To check which products do not have a SKU, sort the table catalog_product_entity by SKU. All the products with no SKU will then be grouped together. You can then fix this issue by manually adding the SKUs to the products in this table (though don't make a habit of directly editing the database - that way madness lies).
How did it happen? Poorly written extensions or product data import tools which don't use Service Contracts, or use direct SQL queries to save data into the database. Service Contracts define repositories which include checks to make sure all entity data is present and correct (including SKU) before attempting to save it. Other product import tools write data directly to the database, bypassing Magento's repositories and import/export adapters and thereby bypassing the data validation they contain too.