Regarding the alternative: I can use the DigiD for some things, such as filling taxes. But not for others that require ID check, such as checking healthcare data. The alternative is to either call, or go in-person indeed.
Regarding the EU ID efforts: I hope it helps. I know there’s also the EIDAS that aims to enable citizens of country A to login in services of country B using country A’s authentication method. For example, I can use the Portuguese login system to login in duo.nl. However, not all websites and countries support this. Only recently DigiD was even approved as a valid EIDAS authentication method. And I personally think that an EU-level interconnected authentication system is still few years away.