I don't like the idea of attaching a lesser thing (such as CPU) to our brai
Do you 'not like the idea' because you think it won't work?
It might not. But effective intelligence is a function of a number of factors--processing speed seems to be one of them.
Currently, we have different sub-processing systems in the brain, and the mind is divided too.
Managing the body and keeping aware of external threats are two semi-automatic subsystems. You react to a possible threat before your conscious of the threat.
Certainly you would require time & training to use such an attached processor, and it's most likely to be used for memory storage & retrieval and specific tasks which can be easily assigned to a computer.
Self-aware machines would be able to interface and handle such tasks much better than a simple computer.
Your cases where a computer doesn't make determinations are wholly off base...computers can and do make such decisions, and faster than people with the exception of visual processing, which we are rapidly accelerating.
A 'split second' for human reaction time is ~500milliseconds on a current generation cpu that is a very long time--time for millions of operations. More on a parallel system.
Computers can and do anything that you can tell them to do--the limitation on what can be done is in the human mind, not the hardware. How fast things can be done depends upon many issues.