Latency and stability are different things. Latency is how long keystrokes or mouse movement take to get to your computer. Instability would manifest as INCORRECT or entirely missed keystrokes or mouse movements. Bluetooth is also more vulnerable to interference from things like microwaves, another thing that might cause instability.

Bluetooth keyboards (usually Logitech) have worked okay for me in the past, but they don't always reliably wake up from sleep and connect quickly when I try to use them. Bluetooth mice are a bigger concern to me, they feel noticed slower and my mouse makes jerky movements. You'll notice that nearly all gaming mice have a dongle so that you can avoid Bluetooth.