Mail, Safari, Apple Music are installed apps defined by default. You cannot set another default email, browser, or music player app. This may change.
Do you want to use Spotify, Deezer or another app on your HomePod without specifying each time which app to use? Many are in this case. Although it is possible to use Apple Music with Alexa by default, the Apple system is more closed and does not allow you to use a third-party app for music.
When you click on a link, it will automatically open Safari. Are you clicking on an email? You will have to go through Mail if you do not copy this email and then open your app.
You can freely use other apps, but you can’t make them your default app.
According to Bloomberg, it could be that, from iOS 14, this could change. Another app for your e-mails, your internet research, your music… Case to follow.