Speakers hung from ceiling on aircraft cable.

Opinion question:

We are thinking of suspending a pair of KEF LS50 speakers from the ceiling using aircraft cable. Do you think having them not rigidly mounted will diminish bass? Will the woofers cause the speakers to move?

David, I did this with a pair of open baffle speakers I made for a friend.
It worked wonderfully however I crossed to a subwoofer at 80 Hz. The
Speakers also weighed 20 lb each. 

The LS 50's are not very big and they do not go very low down. I suspect they will be OK. If you feel them move with bass you can always put a lead sheet on the top of the speaker to weigh it down. I would not use cable. You will have trouble getting the speakers to face in the right direction as the cable is torsionally compliant. Better to use chain it is much less torsionally compliant and will want to stay in one position.
When it's on the floor, it's not rigid, is it?

Ok let me ask this, what are you trying to do? or stop, or figure out?

They will swing, the longer a single tether the further they will swing.

2-4, not so much, actually can stabilize the cabinet, tip it, easy to vacuum under, ay..

Wow, deja vu all over again. Hanging your speakers from the ceining was a common practice when I worked for RogerSound Labs in the 1970s.

Short answer: bad idea. Why?
1. Imaging sucks. Do you enjoy the soundstage from ceiling mounted speakers? Cable suspension is worse.
2. Significant loss of bass response. Maybe not so much a problem with the LS-50s but why make a bad situation worse?
3. Loss of resale value. Trust me, no one wants to buy your speakers with holes drilled into them.
4. Reputational damage. Yours.

Surely a flat platform with a filament at each corner would work, kind of like a child's swing, only don't push it!  Blu-tack speaker to platform.
Newton's third law says no.

The drivers are motors and pushing back and forth against the cabinet. If they are not rigidly held in their 3 dimensional space relative to the listener you will introduce all sorts of artifacts.

In fact, even with stand mounted speakers, mass often helps to improve clarity and performance but your suggestion is even worse than a basic stand mount.