I suspect Im one of the ones you have seen suggesting big numbers. My background is pro audio using speakers like these at their max to fill large area with as much sound as possible so Ill try and clealy explain my rationale for reccomending such large amplifiers
To expand on what @Tvor-ceasar has said yes these speakers are very efficient so in a small room home application you can get alot of SPL for not alot of power however the power increase to SPL increase is exponential so if you take them outside you will very quickly run out of power on the same amplifier that blew your ears out inside. A good real world example is a guitar amp. a 100w amp is only 2x the loudness of a 10w amp but needs 10x the power to achieve that, an approximate rule of thumb we can take from this is 10x the power per 10db increase in SPL. Another thing to note is that the power requirement to produce the same SPL also increase more and more as the frequency gets lower, reducing the low extention of a speaker can allow it to play cleaner and louder on the same sized amplifier
I would say there are 2 options you can take to power the speakers
- get larger PA amp capable of running them properly outdoor and turn the amp down when used indoors
- get a more moderate capacity amp and DSP with adjustable highpass to reduce the bandwidth at higher volume outdoors
Option 1 would be the preferable option but it is going to be more expensive. Any decent quality modern amplifier should be perfectly happy to run underutilised as to turn it down the input signal gets trimmed down in the before hitting the amplification stage
Option 2 you would basically have 2 different highpass(HP) protection filter positions. You will gain SPL outdoor with an amp sized for indoors but you will sacrifice low end extention outdoors. Indoors at lower volumes you would leave the DSP open and use the amps inbuilt HP filter (20hz ish) getting the full designed frequency response of the speaker. Outdoors you would add a DSP HP filter to limit the playing range of the speaker based on the desired SPL. You would have to test and find that DSP HP frequency yourself so I cant tell you how much SPL gain you would achieve this way
With option 1 id be suggesting an amp that can do 1.1x-1.2x rated total RMS wattage, in this instance that is around 1000w RMS per channel
With option 2 Charlies suggestion of 400w-500w seems appropriate to me to be safe with an adjusted HP filter but the bigger you can go on the amp the more bass you will get back when used outdoor
Either option I would reccomend a 2 channel PA amp over a reciever for reasons discussed in this thread https://toidsdiyaudio.com/forums/discussion/best-subwoofer-amp-crown-xti2002-vs-behringer-nu6000dsp-vs-dayton-apa1200dsp/