how can low watt tube amps drive speakers with higher power requirements

The low power amp with say 50 watts cannot harm the speaker able to handle 500 watts, unless maybe if you drive the 50 watt amp so hard that it is clipping a lot. Then if clipping is bad enough the output looks almost like a square wave. This is kind of like, imagine you are doing bench presses. Only instead of the sine wave full lift you do a square wave and try and hold it at half way. How long till your arms are shaking? That's pretty much what happens with speakers. Power pushes the cone out part way, holds it there, distortion increases, a lot of it is very high frequency, and he combination of square waves and extra high frequencies burns out your tweeter. This is why almost always the tweeter goes in these situations. 

Now if you really do use too much power, even really clean power, that is another problem. Because dynamic drivers are a voice coil inside a magnet gap, with a spider and a surround designed to hold the coil so it moves like a piston perfectly straight and on-axis. Which works fine within a certain range. Too much power and the excursion is too great, the spider or surround can flex the wrong way, the coil goes out of alignment, and it doesn't take much the gap is real small, voice coil gets bent and you start hearing a scraping sound, or maybe knock or rattle, depending on what happened. 

Your third failure mode is heat. Power heats the voice coils, and if they get too hot the insulation can burn, leading to a short. Or the coil can deform, leading to scraping, rattling, etc. 

These are the real reasons for giving power ratings. But it's like megapixels with cameras, the last thing that matters is the first thing they feed you. Because too much trouble to explain so you understand what is really going on. 

You are indeed. And you are not alone. Whole lot of guys are missing it. Even ones who should know better. Amplifier watts are just about the least relevant spec in all of audio. 

What really does matter is speaker sensitivity. Because it requires a huge increase in power to play just a little bit louder. 3dB is a small increase, but it requires TWICE the power! Think about that. 10dB, TEN TIMES the power! 

What this means is an amplifier TWICE as powerful will only play a measly 3dB louder. No matter what speakers. That is a fact. 

So if you buy 88dB speakers, they will need 100 watts to play as loud as a 98dB speaker will with only 10 watts. 

This is the reality. Speaker manufacturers find it a whole lot easier to sell tiny little speakers, because they know women control the speaker market. Tiny little speakers are horribly inefficient so they hide this from guys they know are too whipped to do what's right by their audio anyway.

The fact of the matter is no speaker has any power requirements whatsoever. What they mean by this, their convoluted logic, is they know their speaker is so terribly inefficient nobody is gonna be happy with less than 50 watts to bring it up to a reasonable level. So they say 50. Then they also know their speaker is gonna burn out if played loud with a lot of power. So they say 50 to 200 watts. Or something like that. Point being it is all smoke and mirrors. You can safely ignore the whole thing. It is pure BS.

All you need to know is if you buy speakers with sensitivity much below 92dB you are going to start to have a hard time finding an amp you can afford they will sound good with- and the further below 92 you go the harder - and more expensive- this will be. Stay up around 95dB and above, no problem. All kinds of amps to choose from. Some of the very best amps at any price only put out around 10 to 50 watts. Which is all you need, provided only you are smart and avoid anything below about 92. All you need to know.