So it's pretty much good to have the other promotions in your conquering army and have a subset of units promoted through the Drill promotions to act as a mop up unit to clean up after siege unit collateral damage?
That could work, but it works exceptionally well once you have bombers because they can do damage without a lot of risk and weaken a unit to such an extent that it can be destroyed by first strikes alone. However the interception rules for planes have changed and maybe bombing isn't the most cost-efficient way to weaken and destroy an enemy anymore.
Note that the Drill III and Drill IV are especially interesting. Not only because they add a greater number of first strikes than Drill I and II, but also because the jump from 4 to 8 first strikes is more interesting than the jump from 0 to 4. At a certain number of first strikes, it just becomes unrealistic that a (wounded) unit still has hit points left after the first strikes have done their damage.
For example (simplified, but it makes it more understandable): If a first strike unit had a 50% chance to do 20 damage per first strike, then a wounded unit at 50 hitpoints could very well be alive after 3 first strikes. All 3 of them would have to be successful to kill the unit before the real fighting starts (chance 12.5%). However if the unit has 6 first strikes, then the change that 3 of them are successes is pretty likely (chance 65.6%).
If the unit is stronger than the unit it attacks, then it will do more than 20 damage per first strike and the chance to hit for each first strike goes up so you have a bigger chance to kill it before it purely with first strikes.
For instance, if a unit with 6 first strikes has a 70% chance to do 25 damage per first strike, then the chance that a wounded unit at 50 hitpoints survives the first strikes is only 1.1%. So the chance to kill it with first strikes would be 98.9%.
The above is just a simplification of the chance to survive the first strikes, but it does show the strength of a high number of first strikes and the strength of being a bit stronger than the enemy.