There are tons of articles about this on various audio manufacturer websites and audio forums. Most of them recommend the amplifier RMS capacity to be 1.5 - 2 times the speaker's top wattage rating.
You're thinking as an electrical engineer and your logic would most likely be "my amp should not fry/burn my speakers". In reality, the opposite is true. Speakers most often get fried or burnt because of under-powered amplifiers that "clip" i.e. max out and send a pure DC signal to the speaker which damages the speaker driver.
Despite all the "nominal" rating of impedance, the reality is that speakers draw power from the amp in a very very spiky manner. their impedance also drops - a 6 ohm or 8 ohm nominal speaker's impedance will often drop to 3.5 ohms when playing certain audio frequencies. Note that when a speaker presents a 3 ohm load to an amp, the amp has to provide 2-3 times the current and power to the speaker for that frequency. If it cannot produce this spike of current and power, it will clip and risk damaging your speaker.
This is another reason why amp ratings must be higher than the speaker.
Now, to your main concern - with a higher powered amp, will you risk frying your speaker? Yes, there might be an example or two of this where people pushed their speakers and amp to extreme levels for extended periods of time, but this is much more rare than the other scenario that everyone is telling you about of underpowered amps routinely clipping. And if you still have doubts, please read on the internet instead of trying to get answers from this thread.
At any rate, very very few people buy an expensive audio system and then blast it at 100% volume for hours at stretch. If you really want to play music this way, then you should not be looking at hifi audio in the first place. You should look at commercial PA systems and DJ equipment. They are more robustly built to handle those extreme SPL and power levels, and of course with the trade off of sound quality.
Here's an article on this subject by Crown Audio, which makes and supplies amplifiers for professional audio setups, studios etc. They have very specific recommendations for different use cases.
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How Much Amplifier Power Do I Need? | Crown Audio - Professional Power Amplifiers
From the article:
First, define your goal. Do you want to power some loudspeakers so they play as loud as possible without burning out? If so, all you need to read is the section below. Do you want to achieve a certain loudness in a certain venue? If so, skip to the section called Power vs. Application.
How much power can my speakers handle?
You can determine this by looking at the speaker's data sheet. Look for the Nominal Impedance spec. Typically it will be 2, 4, 8 or 16 ohms. Next, look for the loudspeaker specification called Continuous Power Handling or Continuous Power Rating. It might be called IEC rating or Power capacity.
If you can prevent the power amp from clipping (by using a limiter), use a power amp that supplies 2 to 4 times the speakers continuous power rating per channel. This allows 3 to 6 dB of headroom for peaks in the audio signal. Speakers are built to handle those short-term peaks. If you cant keep the power amp from clipping (say, you have no limiter and the system is overdriven or goes into feedback) the amplifier power should equal the speakers continuous power rating. That way the speaker wont be damaged if the amp clips by overdriving its input. In this case there is no headroom for peaks, so youll have to drive the speaker at less than its full rated power if you want to avoid distortion.
If you are mainly doing light dance music or voice, we recommend that the amplifier power be 1.6 times the Continuous Power rating per channel. If you are doing heavy metal/grunge, try 2.5 times the Continuous Power rating per channel. The amplifier power must be rated for the impedance of the loudspeaker (2, 4, 8 or 16 ohms).
Here's an example. Suppose the impedance of your speaker is 4 ohms, and its Continuous Power Handling is 100 W. If you are playing light dance music, the amplifier's 4-ohm power should be 1.6 x 100 W or 160 W continuous per channel. To handle heavy metal/grunge, the amplifier's 4-ohm power should be 2.5 x 100 W or 250 W continuous per channel.
If you use much more power, you are likely to damage the speaker by forcing the speaker cone to its limits. If you use much less power, youll probably turn up the amp until it clips, trying to make the speaker loud enough. Clipping can damage speakers due to overheating. So stay with 1.6 to 2.5 times the speaker's continuous power rating.
Power vs. Application
This section will suggest how big a power amplifier you need to fill a venue with loud, clear sound. Basically, the louder the sound system and the bigger the room, the more power is required. Loudspeakers with high sensitivity need less power than loudspeakers with low sensitivity.
The list below recommends the total amplifier power needed for several applications. Each application has a range of power based on the desired loudness and the typical loudspeaker sensitivity.
In compiling this list, we made the following assumptions:
Typical loudspeaker sensitivity is 85 dB SPL/W/m for home stereos, 95 dB SPL/W/m for small PA speakers, 100-105 dB for medium PA speakers, and 110 dB for large PA speakers.
The recommended power allows for signal peaks of 10 dB for folk, jazz and pop music. Actually the peaks might be as high as 25 dB, but we're allowing for some inaudible short-term clipping.
The recommended power allows for signal peaks of 6 dB for rock music that is highly limited or compressed.
According to Crown's chief amplifier engineer, Gerald Stanley, amplifier continuous power and amplifier peak power are nearly the same. Typically, peak power is only 1 dB higher than continuous power, and depends on peak duration.
Total amplifier power required in various applications
Nearfield monitoring: 25 W for 85 dB SPL average (with 15 dB peaks), 250 W for 95 dB SPL average (with 15 dB peaks)
Home stereo: 150 W for 85 dB SPL average (with 15 dB peaks), 1,500 W for 95 dB SPL average (with 15 dB peaks)
Folk music in a coffee shop with 50 seats: 25 to 250 W
Folk music in a medium-size auditorium, club or house of worship with 150 to 250 seats: 95 to 250 W
Folk music at a small outdoor festival (50 feet from speaker to audience): 250 W
Pop or jazz music in a medium-size auditorium. club or house of worship with 150 to 250 seats: 250 to 750 W
Pop or jazz music in a 2000-seat concert hall: 400 to 1,200 W
Rock music in a medium-size auditorium, club or house of worship with 150 to 250 seats: At least 1,500 W
Rock music at a small outdoor festival (50 feet from speaker to audience): At least 1,000 to 3,000 W
Rock or heavy metal music in a stadium, arena or ampitheater (100 to 300 feet from speaker to audience): At least 4,000 to 15,000 W
Although a rock concert in an arena could be powered by 15,000 watts (allowing only 6 dB of headroom for peaks,) you'll often see large touring sound companies using 80,000 to 400,000 watts total. That much power is needed to handle 20-to-24 dB peaks without any clipping, and to power extra speakers for even coverage of a large area.
If one loudspeaker won't handle the total power required, you need to divide the total power among multiple loudspeakers and multiple amplifier channels. For example, suppose you need 1000 watts to achieve the desired average loudness, but your speakers power handling is 250 watts continuous. You could use a power amplifier of 500 watts per channel. Connect two loudspeakers in parallel on each channel. That way, each speaker will receive 250 watts (not considering the change in amplifier power at different impedances, and not considering cable losses).
Note that if you parallel two speakers, their total impedance is halved. For example, two 8-ohm speakers in parallel have an impedance of 4 ohms. In that case, each speaker would receive half of the amplifier's 4-ohm power.
. Unfortunately, me and people like afj can debate to the ends of the earth and you would still not have an answer 
