The Deliverance Engine massively boosts ur culture on the target planet and temporarily can turn it into something like a culture hub itself. It also gives a 20% damage boost to all allied ships in the area both at the point of impact as well as any other allied ship that jumps in after that for a good long time, long enough to beat the **** out of the enemy.
It is very useful in an assault due to the 20% damage bonus it gives to allied fleets, which can mean the difference between victory and defeat. It can also be used as a way to force the enemy to hold caps and titans in certain locations to prevent planet loss as it'll force the enemy to hold these ships in orbit, or at least panic build culture hubs. Either way, it causes a reduction in effective military strength that can be deployed against you, or a sacrifice in economic viability in the long or short run due to the opportunity loss of those 4 logistics slots.
It should be noted that multiple Deliverance shots don't seem to stack, at least on the damage front.