Sound intensity (measured in decibels) and power (measured in watts) in a speaker system do not have a linear relationship. To get a 3 dB increase in sound intensity, you need to double the wattage. In a speaker system, the connection between sound intensity and power is the speaker sensitivity, which is measured in decibels/watt/meter. The meter term accounts for the distance away from the speaker as sound intensity halves when distance doubles. Total power handling, how much you power you can put into the speaker before it is destroyed, is a completely different metric and has little relation to sound intensity in hi-fi settings.
Two examples:
Joe has a hi-fi stereo system with high efficiency speakers (100 dB/watt/meter per speaker, 100W max) in a dedicated setup where he sits fairly close to his speakers (2 meters). Unforunately, Joe has bad taste in music and generally listens to low dynamic range modern pop/rock/rap (average volume is -6 dBFS).
Sarah has a modern space efficient stereo sub-sat system (85 dB/watt/meter per speaker, 200W max) in a setup where she sits at tv viewing distance away from her speakers (4 meters). Sarah mainly listens to classical and jazz recordings (average volume is -15 dBFS).
Both listen at a responsible level (88 dB average volume).
In this example, Joe's speaker system needs a meager 0.25 watts/channel to get his music not to distort. Sarah's speaker system needs a whopping 128 watts/channel to do the same. This is why amplifier power levels can be important. It can allow for high dynamic range and compensate for distance and/or inefficient speakers. In Joe's case, the fact that his speakers can take up to 100W doesn't matter. His listening habits don't require anything near that much. Sarah is a different case. Since her system needs so much power in order to avoid clipping, max power handling is a big issue. If her speakers could only handle 100W like Joe's, she'd have an issue on her hands.
As far as car subwoofer power levels go, look at an equal loudness curve. The ear is very effective at discriminating against low pitched sounds, so making subwoofer loud enough to sound loud requires a whole lot more power (something like 20-30x more) given comparable efficiencies between the subwoofer and other speakers.