The home office rather notoriously destroyed/never kept its own records of arrivals of commonwealth citizens, which was one of the steps leading to the Windrush scandal.
Many older records only exist in paper form, and often the receipts are good enough. This is especially true when you’re dealing with 3rd party governments. A foreign government is going to put a lot more stock (rightly or wrongly) on a birth certificate that is printed on fancy paper covered in security features than it is to a printout of an email.