Vuetify Version: 2.0.11
Vue Version: 2.6.10
Browsers: Firefox 68.0
OS: Ubuntu undefined
Headers are kept hidden even on mobile when hide-default-header is true
Headers are being displayed on mobile
Normal viewport:

Firefox window resized:

Ran into this today. While waiting on a fix, this can be worked around relatively well by adding this to your styles:
.v-data-table__mobile-row__header {
display: none;
}
.v-data-table__mobile-row__cell {
text-align: left !important;
}
Can see it in action here: https://jsfiddle.net/wzL4y7h8/
Your reproduction is missing v-app
Most helpful comment
Ran into this today. While waiting on a fix, this can be worked around relatively well by adding this to your styles:
Can see it in action here: https://jsfiddle.net/wzL4y7h8/