Is there some way other than ctrl-k to bring up the command palette? Ctrl-k is not particularly touchscreen tablet friendly as it is first necessary to bring up the onscreen keyboard.
Maybe it could be added to the list of quick-action items.
The command palette is never going to work well on mobile. Even if you could bring it up with a button, you'll have to focus a text field, wait for a keyboard to come up, and then type what you want.
At that point, you might as well just tap to navigate.
A command palette is just one of those advantages of having primary keyboard input. And that's something desktop computers accel at and mobile devices fail at.