What I don't understand is why this happens for speakers rated with more watts, compared to the amp rated watts, instead of for those rated with less watts.
That's where
@TLS Guy "more complex...." comes in. He's a doc, not an EE, but he read a lot over many years, you can keep reading and will soon understand more than many audiophiles too.
You are at a good starting point so I would suggest when you do your online Googling/learning, try to focus on reading about voltage and current, instead of watts, then at least you won't get confused by many poster's including TLSGuy's last post about "apparent" power.
On that, basically, understand that a speaker that has the following specifications first, before trying to understand how it's "rated with more watts, compared to the amp rated watts, instead of for those rated with less watts...." that you are now trying to understand:
MAXIMUM OUTPUT
110 dB
That most likely means listening at 1 meter from the speaker, you may get roughly 110 dB of sound pressure level, without hearing unacceptable distortions (or you might, actually, it depends...)
AMPLIFIER REQUIREMENTS
15 - 180W
If you want to know what this mean, you need to ask the manufacturer directly, you may or may not get a reasonably accurate answer, as again, in depends... Manufacturers such as SVS, KEF, B&W, Revel probably might, as long as you can get pass their first level customer support.
A good guess of what that 15 - 180 W mean is probably, that depending on your listening habit (how loud, and the types of music genre etc., and distance, you can get away with an amplifier rated 15 W average into 4 ohms, but 180 W would probably be more appropriate for this speaker, in terms of distortions and longevity.
NOMINAL IMPEDANCE
4 Ω (min. 3.2 Ω)
That is a relatively more meaningful specifications, many speaker manufacturers might just tell you 4, 6, or 8 ohms period, within giving info on the minimum, and/or whether it is a "nominal" value, leaving you to guess.
SENSITIVITY (2.83V/1m)
87 dB
This is better than the format 87 dB/W/1m. It tells you that if your amplifier outputs 2.83 Vrms to the speaker, the speaker will produce 87 dB at 1 m.
Some specifications use the format dB/W/1m, in that case it would be 87 dB/W/m, the problem with that is, as I mentioned many times, it is not a good idea to use the term Watt for speakers, that is basically a voltage sensitive device, so we really don't know how much watt is dissipated in, or consumed by a speaker.
When people say the speaker takes 100 W, we really don't know what they are talking about, other than they probably mean if the amplifier applies the same voltage to a pure resistor of 8, 4, or whatever the spec says the speaker's impedance is, then the amp
would dissipate 100 W in the resistor. I really have no idea, not exactly anyway about the meaning of 100 W speaker. Those who claimed they do, be careful of their rationale or ask for link to the information source such as lab measurements etc.
For now, it may suffice to say, an amplifier driving an electromagnetic transducer (speaker), will deliver current to the speaker, thereby dissipate power in the speaker, but also dissipate power in the amplifier, mainly in the output stages, especially the output devices (such as power transistors), so there really isn't much point in talking about speaker wattage, but that's the way it is, and 99.999% of the consumers are not engineers or scientists, let alone electrical engineers, so it may the better way to begin with anyway, whether I agree or not.
The example speaker specifications I used above is from one of KEF's R series, that's why the information is quite detailed.
I hope it at least give you an idea, without getting too technical, why some of us are saying it can get more complex than you think if you really want to satisfy your curiosity and understand more about the answers given to your apparently simple questions.