Well said, another way of saying it is...first off amps don't output at 4ohm. A better way to look at it is that amps produce a specified amount of power at various impedances (ohms).
Speakers are then built/designed to have a particular resistance (measured in ohms).
Then capacitors that you are referring to, they will block lower frequencies, and what frequencies they block will be determined by the resistance of the speaker. You can look up the charts online if you have already done so.
So the short answer to your question is, the speaker determines the XO point of the cap.
An amp outputs to try and hit a voltages hat is moving with the input signal.
An amp that is rated at 4-ohms can supply enough amperage to a 4-ohm load to drive some amount of watts.
An amp that is rated capable of delivering into a 2-ohm load will be delivering twice the amps (and hence twice the watts).