One datapoint: at least in practice, it used to be impossible to delete an entry in the French INPI database (trademarks and company names) without eIDAS. It forced me to unearth an old unmodified Android phone (I run LineageOS on my main phone).
If you read French:
* https://www.plus.transformation.gouv.fr/experiences/4531155_...
* https://linuxfr.org/users/jch-2/journaux/l-identite-numeriqu...