You have to remember that all a power rating implies is that the speaker will be able to see 60W continuously without thermal or mechanical failure. It has absolutely no bearing or implication on what amp to use. Can the said speaker see more power? Of course it can, but perhaps not continuously. It can probably handle 120W without a problem in transients. But the manufacturer cannot guarantee this, so the claim is not made. When rating speakers, RMS is an average (root mean square) of the total power seen and it implies that the speaker can handle that amount of power continuously.
Remember, when you hook up a speaker to a 120W RMS rated amp, the amp is never producing 120W RMS unless you are playing a contuous sine wave with the amp turned all the way up. Therefore, the speaker never actually sees 120W continuously. With a 120W RMS amp, the speaker may only be seeing 50W on average and up to 130W in transients. Still, most of the time the speaker will rarely see the rated power of the amp for long periods of time. Of course, that means that a 60W RMS amp will never deliver 60W RMS to the speaker, unless you are listening to sine waves.
Also keep in mind that the overall response, distortion, and tonality of the speaker does NOT change depending on the power input. It is fairly constant (with the exception of thermal issues). So it is incorrect to say that the speaker won't sound as good as possible on less power. Technically it just won't be as loud. However, dynamics DO affect the perceived sound quality and amplifier power headroom is key here. A 120W RMS amp will typically have better dynamics than a 60W RMS amp if both are producing 60W RMS. Furthermore, a cheap 60W amp pushing 60W will run hot and distort more than a 120W RMS amp running cooler well below its threshold. You should ALWAYS consider an amp that will give you ample head room especially if you will be listening frequently at high levels. Contrary to popular practice, you don't have to be squeezing every last drop out of your amplifier at the lowest impedance possible. Instead you should buy an amp that is capable of more power than you need and drive it at moderate levels. This is especially true if you are trying to maintain sound quality at loud listening levels.
So to answer your question, the power rating has little to do (at least directly) with what amplifier to use. It is a rating of how much power the speaker can see and should not determine the power capabilities or quality of your amplifier.