I've had this problem too.
I solved this problem. I'm typing the height value and I use align-center, justify-center and fill-height* classes in <v-list-item>
<v-list height="..vh">
<v-list-item class="px-0 align-center justify-center fill-height">
I use it in my project as follows:
<v-navigation-drawer permanent expand-on-hover>
<v-list height="90vh">
<v-list-item class="px-0 align-center justify-center fill-height">
<v-list-item-content>
<v-list-item link>
<v-list-item-icon>
<v-icon>mdi-home</v-icon>
</v-list-item-icon>
<v-list-item-title>Lorem ipsum</v-list-item-title>
</v-list-item>
<v-list-item link>
<v-list-item-icon>
<v-icon>mdi-home</v-icon>
</v-list-item-icon>
<v-list-item-title>Lorem ipsum</v-list-item-title>
</v-list-item>
<v-list-item link>
<v-list-item-icon>
<v-icon>mdi-home</v-icon>
</v-list-item-icon>
<v-list-item-title>Lorem ipsum</v-list-item-title>
</v-list-item>
</v-list-item-content>
</v-list-item>
</v-list>
</v-navigation-drawer>
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