Jellyfin is (in part) about showing off all of your media in one place. When you first open the app having "favorites" there eating that screen space detracts from that. There are a few redundancies and perhaps unnecessary buttons that take up more space than necessary on the home screen, especially on mobile.
edit:
Revised and more concise after discussions here and on matrix:

We should keep UI consistent between screens, so I'm against having the tabs moved up on home (Besides, it could get messy on smaller screens).
The headerbar hides itself on mobile anyway, so it's a non issue.
The hamburger menu should be shown though, for sure.
the tabs already move up on non-mobile displays. i'm not advocating moving them up on mobile. i am advocating moving "favorites" up in the form of a "heart" button to free up valuable space.
the headerbar does not hide itself automatically on mobile but DOES on the non-mobile display.
CSS code provided by thornbill will bandage this but still leaves a massive gap.
"
@media all and (max-width: 62.5em) {
.noHomeButtonHeader .headerTabs {
display: none;
}
}
"

the tabs already move up on non-mobile displays. i'm not advocating moving them up on mobile. i am advocating moving "favorites" up in the form of a "heart" button to free up valuable space.
_This is just quick CSS test._

In this case we need to extract favorite in its own page.
the headerbar does not hide itself automatically on mobile but DOES on the non-mobile display.
it should hide on scroll down
_This is just quick CSS test._
This isn't good usability wise, though. It suggests you can favorite this page, since that's what that icon does on every other screen.
If we move Favorites into the hamburger menu from the home screen, here's the space that will be reallocated to displaying media items (taken from Android 1.0.0:
Before:

After:

Most helpful comment
This isn't good usability wise, though. It suggests you can favorite this page, since that's what that icon does on every other screen.