The act of connecting an amplifier that is capable of putting out more or less rms wattage than the speaker's rms rating does not and can not in and of itself cause speaker failure. Speakers fail because of what the user does with the controls at the head unit and the amp.
Think of it this way: I could put a 35 watt amplifier channel to a 180 watt speaker, play it with the volume at 5 all day long every day for years, and probably never cause a problem.
I could also connect a 500 watt rms amplifier to that same 180 watt speaker and play it with the volume at 5 all day long every day for years, and probably never cause a problem.
And the act of connecting, say a 50 watt speaker to either a 30 or a 55 watt amplifier does not cause that speaker to magically burst into flames instantanously. Ignore the numbers on the speaker and amplifier box. You may have 100 watts per channel but at any given moment you may actually be giving that speaker as few as 20 and it's quite possibly that it has never even seen the full 100.
In the first case if the 180 watt speaker isn't very sensitive things won't get loud enough so alot of people, even alot of professional installers, will crank the gain some to make up for it and try to get the system to reach maximum volume more quickly. In combination with this alot of people will crank their head unit until it's putting out a distorted signal, which is amplified before being sent to the speakers. Thermal failure is a very likely result.
In the second case if I set the gain to deliver that full 500 watts at my head unit's maximum undistorted volume setting then keep the volume in that region continuously, there is a good chance that that speaker will get overdriven and mechanical failure could result. Thermal too, but less likely in this situation because the building up of excess heat in the voicecoils is not as continuous as it is with a severely clipped signal.
Subs can take it more easily than door speakers, and how quickly you reach meltdown with a door speaker will depend on how much more you're delivering to it than what it's rated for and simultaneously how low you're trying to make it play.
Im no expert but Ive done some reading. The reality of how an amplifier delivers power and under what circumstances a speaker's ability to handle it is tested really is quite different from the common textbook advice to match RMS ratings that you will hear in most car audio shops.
So nope, neither in and of itself automatically causes melt down but in my opinion it's better to overpower than to underpower. You want to make sure you get sufficient loudness to appreciate the detail in your music without straining anything. There are people who connect speakers to amplifiers rated for 2,3, or even 4 times that speaker's rms rating. Now I assume we're talking about really good speakers and clean power. If you understand that an amplifier's power delivery is not flat and linner when you play dynamic music, and you back off on the gains and volume enough that the speaker is unlikely to spend any real amounts of time during normal listening exceeding its true limits, you can get loud, quality sound that is clean right up to the uppermost peaks and highest volumes without having to raise your gain and accept any distortion in your system.
It's all about how loud you need things so you can appreciate your music without making adjustments that will blow something up, and whether you know how to properly 'overpower' a speaker.