Praxis might have exploded ‘away’ from Qo'noS.
That would actually make things worse. If the mass blasts outward from the planet, then it will still have the same lateral orbital velocity. It'll still be in the same orbit, but with greater eccentricity, i.e. on a more elliptical path -- getting further out from the planet at apoapsis, but coming in closer to the planet at periapsis. So that would actually make the particles
more likely to collide with the planet. (Imagine, say, pushing sideways on someone swinging on a swingset. It'll just make their swing more wobbly.)
The way to get something out of orbit entirely is to accelerate it
forward. As it gains orbital velocity, it rises into a higher orbit, or leaves orbit entirely if it goes fast enough. But if you accelerate most of the moon's mass forward, then Newton's Third Law means that the big surviving chunk of Praxis will be
decelerated and fall into a lower orbit. Which, again, could potentially make things far worse if it's decelerated enough for its orbit to decay.
I believe that over the proceeding years in order to protect Qo'noS the Klingons probably constructed an artificial moon using the remains of Praxis as a building frame so that they could stabilise the planets tides and weather patterns.
It's highly implausible that a civilization at the Klingons' or Federation's level of advancement could artificially construct something massive enough to have a gravitational effect like that. Note how 80 years later in "Deja Q," the
Enterprise struggled to move a much smaller asteroidal moon. (I suppose a Genesis device could potentially do it, given the magical abilities shown for it in TWOK, but Genesis was a political hot potato that was apparently outlawed, given how it was never referenced after TVH.)
Besides, the tide and weather patterns would eventually stabilize on their own once the mass of the moon debris settled into a ring around the planet. They'd be different from before, but they'd settle down over time. As with our current need to adapt to irreversible climate change, the goal would have to be to adjust to the new status quo, not try to recreate the old one.
The fact that Praxis had been cracked open and exposed in such a way would mean that the raw materials would be even more readily available to mine, and the moons core could have been used as a power source.
It was the dilithium within the moon that exploded, so there's presumably none of it left. Although certainly the remains would be quite hot, so you could use it as a thermal energy source.
On the same subject, does anybody know where the Romulans made their new homeworld after the destruction of the Romulan sun or did they become a nomadic species? Perhaps they all moved to Vulcan? Of course, both Romulus and Remus were destroyed so the Remens would need a new homeworld too.
Picard season 1 seemed to indicate that they'd resettled on multiple worlds, and
Discovery implied that they were essentially without a singular homeworld until they reconciled with the Vulcans and came together on Ni'Var (the planet formerly known as Vulcan).
