Purpose of power handling in the specs?

They likely assume the worst case - no room reflections, no second speaker and at least 2m distance (-6dB).  That makes 83dB/1W at 2m.  50W will get you +17dB making it 100dB at 2m and that's what they likely target.  As for the higher spec of 200W it is maximum that speaker can take without damage.

In your situation you will likely get +3dB from the second speaker and +3dB from room reflections equal to 89dB/1W at 2m (2m cost you -6dB).  7W will get you +8.4dB resulting in 96.4dB/7W at 2m - not bad.

Correction: 89 + 8.4 = 97.4

Maybe part tradition and part guidance. I have typically run speakers with twice the power their rating recommended. Not going for loud but impactful.

I think the guidance is to give a very uninformed consumer something to hang their hat on. So, as an uniformed consumer you buy a cheap $200 amp with 20 wpc and try to make these power guzzling towers sound good… they have given guidance that this was not going to turn out well.

Informed audio folks generally ignore most all of the published stuff… or at least look for anything odd… then look at efficiency and listen to what they sound like. I don;t think I payed attention to power handling in any speaker I have bought in 40 years at least.

You answered your own question. It's how much power the speakers can handle.

rated to handle between 50-200 watts of power

 Shocking isnt it. 

Yes, it is electricity after all.