That said, if there where minimal atmosphere then the effects your talking about become a larger issue. Atmosphere is largely a function of solar wind and volcanic activity which relates to the isotopes in a planets core making this hard to predict.
If the oxygen and nitrogen freezes and snows down in the dark side (-220 C or so), the warm side can't have atmosphere either.
Unless there is some way tidally locked planet can have stable air or sea convection between the sides. I don't think they have.
You have to watch out though - make your mountains too high, and you shift your center of gravity, and now your mountains are no longer elevated.
In this case, the ice is building up in such a way to make the planet even longer in the direction that tidal locking already had elongated it. The effect of which is that tidal locking would get stronger; not weaker.
I don't think it matters too much that it'd be icy on one side and rocky on the other; I think it matters more that it's oblong. But even supposing it does matter, if your intuition is that the more-dense end would want to fall towards the star, then that'd be the rocky end; not the icy end. Yes, the icy end got heavier supposing you measure from the rocky planet's center. But if you shift your frame of reference to be the planet's center of mass, then both halves of course kept exactly 50% of the mass; the densities are what shifted.
The issues with valuable resources running away and not coming back is a serious one even for Earth, which I think might surprise some people. The geological carbon cycle [1] in particular is one that may surprise people who have not encountered it before, or not thought about it in terms of extraterrestrial life. On geological time scales it's surprisingly easy for entire important elements to go find themselves a low-energy configuration they like and disappear from any putative biosphere. The issues with a tidally-locked planet providing such solutions to "all gasses liquids" is merely an extreme example of the case, and really makes one wonder how it would be possible for such a planet to stay "stirred" enough for life to have access to what it needs to develop.
[1]: https://en.wikipedia.org/wiki/Carbon_cycle#Geological_carbon...
If the 'central' planet has 6 close neighbours of equivalent size in resonant orbits would this not provide a very large amount of 'stirring'? These planets are also much more massive than Europa which is only 0.008 times the mass of the Earth compared to ~.6 and ~1.3 Earth masses for the ones in the habitable zone. They may have a more substantial mantle and core, possibly global magnetic fields and definitely more gravity to hold on to any fugitive gasses.
Considering geological timescales, this system is also billions of years younger than our own, potentially only a little over 500 million years old. The processes you draw concern to may simply not have had time to play out yet.
I'm also not convinced that the atmosphere would be cold enough to freeze out gasses on the night side if there were significant oceans or enough atmospheric circulation to transfer heat from the day side.
But we won't really know until we go look at a planet like this, because we don't have one locally to look at. (Plenty of tidally-locked bodies, plenty of bodies with volatiles and enough energy to keep them moving, I'm pretty sure nothing in the Solar system with both.)