Question Exomoons around tidally locked planets

If a planet is tidally locked to its star does that reduce the likelihood that its moons would be habitable?
Good question. I'm guessing the dynamic forces would play havoc with the orbit, but it's only a guess.

But even if it survives in the short term, it won't in the long term.

As a planet loses its rotation rate in becoming tidally-locked, the orbiting moon would eventually be orbiting faster than the rotation rate of the planet. This will cause the tidal stress to drag the moon into the planet.

The Moon, for instance, is moving outward because of the faster rotation rate of Earth. [John Darwin (son of Charles) seems to have been the first to discover this.]
 
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Couldn't a locked planet ying and yang a little for a moon? Or maybe I should ask couldn't a moon still ying and yang a locked planet a little?

And not to get off subject, but you guys are the moon guys, so I read something that surprised me.

Are most of the moons in our system locked in their orbits like our moon is?
 
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Are most of the moons in our system locked in their orbits like our moon is?
I would think this is true for all those that a modest telescope could see. IOW, the very small and distant moons will take forever to lock.

It's worth noting that Phobos, with its orbit period faster than the rotation rate of Mars, is spiraling inward and will crash, but not soon.