this is not true. in our jurisdictions we have provision to claim refund on taxes paid arising from supplies made to certain category of customers. this refund can be claimed any time before September month of the next financial year. in such cases we need to present the authorities with an application for refund along with copies of respective invoices. if the tax identifier is not present in these invoices, they are considered invalid since they do not meet the legal invoice requirements.
also, we are required by law to maintain records for atleast 6 years during which period we will need these invoices to be presented to the authorities when demanded.
this is a general requirement and not restricted to Greece. all custom fields related to the customer are supposed to be displayed under the customer details on a transaction. this is already considered as an idea.