Is there a penalty for changing the approach procedure after accepting one? For example: If you request a visual approach and get approved, but you meant to request an ILS approach, are you not allowed to change it?

Is there some type of penalty for changing approaches after you've already received one?

For example in the video, "PilotsEYE.tv - A380 Landing KSFO San Francisco", the copilot misread a visual approach as ILS, and was given the ILS, but despite the captain's disapproval, they didn't make another call requesting the change.
There is no penalty per se, but visual approaches in particular have lower separation requirements, so having to switch you back to a non-visual approach may require ATC to make corrections (e.g. delay vectors, speed control or, in extreme cases, a missed approach), which may feel like a penalty.