What:
A setting in the mod settings tab that enables playing with unmodified, vanilla movement speeds.

Why:

If I understand correctly, when you play on a controller using Controllable mod, your in-game movement speed will be influenced by the analog stick positions on the controller, so you can move more smoothly and gradually, similar to how movement in typical gamepad-supported games works. It's not a typical behavior for a player using keyboard in Minecraft Java. Java players when being in an unobstructed terrain have one of those fixed speed- it's either no movement if "W" key isn't pressed, standard walk speed if it is, or sprint speed, there are no states between though.

The problem comes when you're playing on servers that have anti-cheat systems to detect unusual movement behavior. These systems might pick up on the different movement speeds caused by the Controllable mod and flag it as something suspicious.

In the practice, player with the mod for example might not be able to move if his/her speed is unusual.
An example server with anti-cheat conflicting with the mod: earthmc.net (1.19.4, the behavior can be noticed even in the lobby, no need to wait in the queue)

Additionally some anticheats restrict player's movement to only the directions attainable by pressing the wasd keys (8 possible directions), whilst the analogue stick on the controller allows for many more degrees of motion, causing the anticheat to trigger and block the player from moving.

As someone who plays on servers with that kind of anticheat, I would also love a toggle for this sort of thing.