Correct questions should be "why some speakers need more powerful amps whereas some other speakers don't?" Because choice of a speaker is a highly personal one like finding your spouse. Once you find the speaker of your choice, next you try to assemble rest of the equipment including the amplifiers to get the "best possible" sound from it.
Two factors determine whether you need a powerful amp or not: Internal impedance and sensitivity of the speaker. If you have highly efficient speakers >90dB, then you don't need a powerful amp. If you have an inefficient speaker <90dB with impedance dropping below 2 or 3 ohms, then you will need an amplifier that can supply current at these loads, i.e., more powerful amp.
There are many variations in between these two scenarios, but you get the idea. The nominal impedance 8 ohm or 4 ohm does not tell you the whole story. Internal impedance change with frequency and can be resistive only at resonance frequency, but rest of the time it is either capacitive or inductive. Some speakers have a nominal impedance of 4 ohms, but minimum impedance at certain frequencies can drop below 3 ohms or even 2 ohms! So amplifier need to provide sufficient currents to these inductive/capacitive loads and at the same time should provide enough dynamic currents for the music.
As you can see, we can only decide what works best by listening. In the end, only you can decide what is best for you. These are just guidelines so that one can navigate and resolve any inadequacy in the audio chain.
