PS4: Mouse doesn't work when hot-plugged while the game is running

Apparently if you plug in a mouse while the game is running, it does not work in-game.

Time: Irrelevant
Frequency: Always
World name: Irrelevant
Character name: Irrelevant
NPC name: Irrelevant
Monster name: Irrelevant
Class/Level: Irrelevant
Party or solo: Irrelevant
In-game time: Irrelevant
Area and coordinates: Irrelevant
Steps:
1. Make sure your mouse is disconnected from the PS4
2. Open FF XIV from the home screen
3. Log in and select a character
4. After the game loads, plug in a mouse
5. Move the mouse

Expected results:
The cursor on screen is expected to move with the mouse.

Actual results:
Nothing happens. The PS4 does report that a mouse is connected, and I can see the mouse power up, but moving it doesn't do anything.

Regression:
This worked correctly in the PS3 and Windows versions of the game.

Workaround:
The mouse does move correctly if it was connected prior to starting the game.

Model Number of the PlayStation®4 You Are Using
- Model Number: There's only one in North America

Information About the Peripherals You Are Using
-Type: USB mouse
-Maker: Logitech
-Model Number: M-BD58